arxiv_id
stringlengths 11
18
| title
stringlengths 6
223
| abstract
stringlengths 3
2.1k
| subjects
stringclasses 151
values | scrubbed_comments
stringlengths 2
1.33k
| category
stringclasses 13
values | __index_level_0__
int64 0
14.6k
|
|---|---|---|---|---|---|---|
0807.3369v46 | A new look at Bell's inequalities and Nelson's theorem | In 1985, Edward Nelson, who formulated the theory of stochastic mechanics, made an interesting remark on Bell's theorem. Nelson analysed the latter in the light of classical fields that behave randomly. He found that if a stochastic hidden variable theory fulfils certain conditions, the inequality of Bell can be violated. Moreover, Nelson was able to prove that this may happen without any instantaneous communication between the two spatially separated measurement stations. Since Nelson's article got almost overlooked by physicists, we try to review his comments on Bell's theorem. We argue that a modification of stochastic mechanics published recently by Fritsche and Haugk can be extended to a theory which fulfils the requirements of Nelson's analysis. The article proceeds to derive the quantum mechanical formalism of spinning particles and the Pauli equation from this version of stochastic mechanics. Then, we investigate Bohm's version of the EPR experiment. Additionally, other setups, like entanglement swapping or time and position correlations, are shortly explained from the viewpoint of our local hidden-variable model. Finally, we mention that this theory could perhaps be relativistically extended. | Quantum Physics (quant-ph) | The stochastic model presented in this article was defect. The parts of this work that are correct are now in a separate article on arxiv.org | factual/methodological/other critical errors in manuscript | 207 |
0807.3531v2 | Classical theory of second-harmonic generation from magnetic metamaterials | Strong second-harmonic generation has recently been experimentally observed from metamaterials consisting of periodic arrays of metal split ring resonators with an effective negative magnetic permeability [Science, 313, 502 (2006)]. To explore the underlying physical mechanism, a classical model derived from microscopic theory is employed here. The quasi-free electrons inside the metal are approximated as a classical Coulomb-interacting electron gas, and their motion under the excitation of an external electromagnetic field is described by the cold-plasma wave equations. Through numerical simulations, it is demonstrated that the microscopic theory includes the dominant physical mechanisms bothqualitatively and quantitatively. | Materials Science (cond-mat.mtrl-sci) | sign errors in equations | factual/methodological/other critical errors in manuscript | 208 |
0807.3579v3 | Thermodynamic consistency and fast dynamics in phase field crystal modeling | A general formulation is presented to derive the equation of motion and to demonstrate thermodynamic consistency for several classes of phase field models at once. It applies to models with a conserved phase field, describing either uniform or periodic stable states, and containing slow as well as fast thermodynamic variables. The approach is based on an entropy functional formalism previously developed in the context of phase field models for uniform states [P. Galenko and D. Jou, Phys. Rev. E {\bf 71}, 046125 (2005)] and thus allows to extend several properties of the latter to phase field models for periodic states (phase field crystal models). In particular, it allows to demonstrate the concept of thermodynamic consistency for phase field crystal models with fast dynamics. | Materials Science (cond-mat.mtrl-sci) | This paper has been withdrawn due to incompleteness | incomplete exposition or more work in progress | 209 |
0807.3677v2 | A bootstrap method for estimating bias and variance in statistical multispecies models using highly disparate data sets | Statistical multispecies models of multiarea marine ecosystems use a variety of data sources to estimate parameters using composite or weighted likelihood functions with associated weighting issues and questions on how to obtain variance estimates. Regardless of the method used to obtain point estimates, a method is needed for variance estimation. A bootstrap technique is introduced for the evaluation of uncertainty in such models, taking into account inherent spatial and temporal correlations in the data sets thus avoiding many model--specification issues, which are commonly transferred as assumptions from a likelihood estimation procedure into Hessian--based variance estimation procedures. The technique is demonstrated on a real data set and used to look for estimation bias and the effects of different aggregation levels in population dynamics models. | Applications (stat.AP) | Submitted for formal publication. Withdrawn due to journal requirments | administrative or legal issues | 210 |
0807.3859v2 | Groupoid actions as quantale modules | For an arbitrary localic etale groupoid G we provide simple descriptions, in terms of modules over the quantale O(G) of the groupoid, of the continuous actions of G, including actions on open maps and sheaves. The category of G-actions is isomorphic to a corresponding category of O(G)-modules, and as a corollary we obtain a new quantale based representation of etendues. | Category Theory (math.CT) | This preprint has been withdrawn because its contents are now included in version 3 of arXiv:0807.4848 | subsumed by another publication | 211 |
0807.3934v2 | Explicit Construction of a Robust Family of Compact Inertial Manifolds | A construction of a robust family of compact inertial manifolds is presented. The result aims to complete an analysis of certain types of attracting sets for a class of dissipative infinite dimensional dynamical systems. Application to a hyperbolically relaxed Chaffee-Infante reaction diffusion equation is also discussed. | Analysis of PDEs (math.AP) | This paper has been withdrawn by the author | reason not specified | 212 |
0807.4104v3 | On a remark by Y. Namikawa | The aim of the present paper is on the one hand to produce examples supporting the conclusion of Y. Namikawa in Remark 2.8 of \cite{N} and improving considerations of Example 1.11 of the same paper. On the other hand, it is intended to give a geometric interpretation of the rigidity properties of some trees of exceptional rational curves, as observed by Namikawa, which can be obtained by factorizing small resolutions through nodal threefolds. | Algebraic Geometry (math.AG) | This paper has been withdrawn because it has been superseded by arXiv:1203.1500 and the just submitted paper "[REDACTED-NAME]'s fiber products", arXiv:1211.6329 | subsumed by another publication | 213 |
0807.4110v2 | Analytic equivalence of geometric transitions | In this paper \emph{analytic equivalence} of geometric transition is defined in such a way that equivalence classes of geometric transitions turn out to be the \emph{arrows} of the \cy web. Then it seems natural and useful, both from the mathematical and physical point of view, look for privileged arrows' representatives, called \emph{canonical models}, laying the foundations of an \emph{analytic} classification of geometric transitions. At this purpose a numerical invariant, called \emph{bi--degree}, summarizing the topological, geometric and physical changing properties of a geometric transition, is defined for a large class of geometric transitions. | Algebraic Geometry (math.AG) | This paper has been withdrawn because superseded by arXiv:1211.6369 and arXiv:1304.1695 | subsumed by another publication | 214 |
0807.4715v2 | Eventually Expanding Maps | In this paper we show that the piecewise linear map f(x) = px for x in [0,1/p], and sx-s/p for x in (1/p,1], p > 1, 0 < s < 1 which has an expanding, onto branch and a contracting branch is eventually piecewise expanding and exact. | Dynamical Systems (math.DS) | This paper has been withdrawn by the author due to a crucial sign error. The correct version of the paper is published in [REDACTED-NAME] [REDACTED-NAME]/Sept issue 2011 | subsumed by another publication | 215 |
0807.4764v6 | Jet schemes, invariant chiral differential operators, and Howe duality | This paper has been withdrawn due to an error in the proof of Theorem 5.3. | Representation Theory (math.RT) | This paper has been withdrawn due to an error in the proof of Theorem 5.3 | factual/methodological/other critical errors in manuscript | 216 |
0807.4971v3 | The Mixing Matrix for a 3+2 Model | In this work we present the characterization of the mixing matrix when the mass matrix is considered, without seesaw, for 3+2 models like. | High Energy Physics - Phenomenology (hep-ph) | This paper has been withdrawn by the author due to a crucial error | factual/methodological/other critical errors in manuscript | 217 |
0808.0383v2 | An Overview of Mixture Models | This paper has been withdrawn. With the advancement of statistical theory and computing power, data sets are providing a greater amount of insight into the problems of today. Statisticians have an ever increasing number of tools to attack these problems, some of which can be implemented in the area of mixture modeling. There is a great deal of literature on mixture models and this work attempts to provide a general overview of the subject, including the discussion of relevant issues and algorithms. The reader can hope to gain a broad understanding of concepts in mixture modeling and find the references cited within as a valuable resource for the next stage of their research. | Statistics Theory (math.ST) | Portions of this review article will be incorporated into a future manuscript | subsumed by another publication | 218 |
0808.0613v4 | Proofs On Arnold Conjectures | In this article, we give proofs on the Arnold Lagrangian intersection conjecture on the cotangent bundles, Arnold-Givental Lagrangian intersection conjecture, the Arnold fixed point conjecture. | Symplectic Geometry (math.SG) | This paper contains a gap. This submission has been withdrawn by the author. | incomplete exposition or more work in progress | 219 |
0808.0653v4 | On the formal grade of finitely generated modules over local rings | Let \fa be an ideal of a local ring (R,\fm) and M a finitely generated R-module. This paper concerns the notion \fgrade(\fa,M), the formal grade of M with respect to \fa (i.e. the least integer i such that {\vpl}_nH^i_{\fm}(M/\fa^n M)\neq 0). We show that \fgrade(\fa,M)\geq \depth M-\cd_{\fa}(M), and as a result, we establish a new characterization of Cohen-Macaulay modules. As an application of this characterization, we show that if M is Cohen-Macaulay and L a pure submodule of M with the same support as M, then \fgrade(\fa,L)=\fgrade(\fa,M). Also, we give a generalization of the Hochster-Eagon result on Cohen-Macaulayness of invariant rings. | Commutative Algebra (math.AC) | This paper has been withdrawn by the authors, because it has been included as a section in arXiv:0807.5042. | subsumed by another publication | 220 |
0808.1000v3 | Fitness Landscape Analysis for Dynamic Resource Allocation in Multiuser OFDM Based Cognitive Radio Systems | This paper has been withdrawn. | Information Theory (cs.IT) | This paper has been withdrawn. | reason not specified | 221 |
0808.1001v2 | Happy places or happy people? A multi-level modelling approach to the analysis of happiness and well-being | This paper aims to enhance our understanding of substantive questions regarding self-reported happiness and well-being through the specification and use of multi-level models. To date, there have been numerous quantitative research studies of the happiness of individuals, based on single-level regression models, where typically a happiness index is related to a set of explanatory variables. There are also several single-level studies comparing aggregate happiness levels between countries. Nevertheless, there have been very few studies that attempt to simultaneously take into account variations in happiness and well-being at several different levels, such as individual, household, and area. Here, multilevel models are used with data from the British Household Panel Survey to assess the nature and extent of variations in happiness and well-being to determine the relative importance of the area (district, region), household and individual characteristics on these outcomes. Moreover, having taken into account the characteristics at these different levels in the multilevel models, the paper shows how it is possible to identify any areas that are associated with especially positive or negative feelings of happiness and well-being. | Applications (stat.AP) | This paper has been withdrawn by the authors as it presented work in progress at the time. A significantly revised and improved version of this work has now been published in 2012 in the journal [REDACTED-NAME] [REDACTED-NAME], vol 35(1), pp 70-102 | incomplete exposition or more work in progress | 222 |
0808.1298v2 | Non Commutative Metrics on Quantum Families of Maps | We show that any quantum family of maps from a non commutative space to a compact quantum metric space has a canonical quantum semi metric structure. | Operator Algebras (math.OA) | This paper has been withdrawn by the author due to a mistake about Theorem 11 | factual/methodological/other critical errors in manuscript | 223 |
0808.1402v3 | A Proof of the Hodge Conjecture | In this paper, we give a proof of the famous Hodge conjecture. | General Mathematics (math.GM) | This paper contains a gap. This submission has been withdrawn by the author. | incomplete exposition or more work in progress | 224 |
0808.1852v2 | The Meccano of life | This article is interested in the origin of the genetic code, it puts forward a scenario of a simultaneous selection of the bases and amino acids and setting up of a correlation between them. Each amino acid is associated with a pair of its own kind, called the binding pair and each binding pair is associated with the codon(s) corresponding to the same amino acid. An explanation is also proposed about the origin of the start and stop codons. | Biomolecules (q-bio.BM) | paper withdrawn by the author due to some errors | factual/methodological/other critical errors in manuscript | 225 |
0808.2690v3 | Complex manifolds with ample tangent bundles | Let $M$ be a close complex manifold and $TM$ its holomorphic tangent bundle. We prove that if the global holomorphic sections of tangent bundle generate each fibre, then $M$ is a complex homogeneous manifold. It implies that every irreducible close Kähler manifold with ample tangent bundle is isomorphic to the projective space. This provides an alternative proof of Hartshore's conjecture in algebraic geometry in characteristic zero and Frankel's conjecture in Kähler geometry. These two conjectures were completely proved by Mori, Siu and Yau. Our proof is quite different from theirs and depends on the complex version of Chow-Rashevskii theorem in Carnot-Caratheodory spaces. | Algebraic Geometry (math.AG) | This paper contains a gap. This submission has been withdrawn by the author. | incomplete exposition or more work in progress | 226 |
0808.2859v4 | Homotopy invariance of higher signatures | We prove that the higher signature for any close oriented manifold is a homotopy invariant. | Geometric Topology (math.GT) | This paper contains a gap. This submission has been withdrawn by the author. | incomplete exposition or more work in progress | 227 |
0808.2967v2 | Continuous Bounded Cohomology of Topological Semigroups | We define a cohomology theory for topological semigroups, with seminormed cohomology groups. Our theory can be considered as a topological version of bounded cohomology of discrete semigroups. | Functional Analysis (math.FA) | This paper has been withdrawn by the author. It was announced me that there is a very advanced book: "[REDACTED-NAME], Continuous bounded cohomology of locally compact groups". I found that many results of my paper on topological semigroups are simple generalizations of the results of Monod's book. So, I withdraw the paper | subsumed by another publication | 228 |
0808.3237v2 | The role of Dirac equations in the classical mechanics of the relativistic top | A rigorous \textit{ab initio} derivation of the (square of) Dirac's equation for a single particle with spin is presented. The general Hamilton-Jacobi equation for the particle expressed in terms of a background Weyl's conformal geometry is found to be linearized, exactly and in closed form, by an \textit{ansatz} solution that can be straightforwardly interpreted as the "quantum wave function" $\psi_4$ of the 4-spinor Dirac's equation. In particular, all quantum features of the model arise from a subtle interplay between the conformal curvature of the configuration space acting as a potential and Weyl's "pre-potential" closely related to $\psi_4$, which acts on the particle trajectory. The theory, carried out here by assuming a Minkowsky metric, can be easily extended to arbitrary space-time Riemann metric, e.g. the one adopted in the context of General Relativity. This novel theoretical scenario, referred to as "Affine Quantum Mechanics", appears to be of general application and is expected to open a promising perspective in the modern endeavor aimed at the unification of the natural forces with gravitation. | Quantum Physics (quant-ph) | A new improved version of this paper was posed on july 15 2011. The new abstract is above | subsumed by another publication | 229 |
0808.3280v3 | Photon blockade and nonlinear effects for a quantum dot strongly coupled to a semiconductor microcavity | Our model comprehensively simulates modern nanoscale semiconductor microcavities incorporating cavity quantum electrodynamics within both the weak and strong coupling regimes, using on-resonant laser excitation and nonresonant excitation due to a wetting layer. For weak coupling, the most significant effect is photon antibunching with nonresonant emission. We investigate how the antibunching characteristics change as the cavity finesse is increased towards the strong coupling regime. Antibunching can also be observed in a strongly coupled system with resonant excitation, using the photon blockade mechanism which has been demonstrated in atom systems. We calculate what cavity parameters are required to observe this effect. Experimentally these studies are equivalent to nonlinear pump probe measurements, where a strong pump, either resonant or nonresonant, is used to excite the coupled system, and the resulting state is characterized using a weak, resonant probe beam. | Materials Science (cond-mat.mtrl-sci) | 5 pages, 5 figures, OECS conference 2007, Sicily, Italy the paper is withdrawn due to a crucial correction on one of the graphs which has been successfully adjusted before acceptance in Phys. Rev. B | factual/methodological/other critical errors in manuscript | 230 |
0808.3386v4 | Linear Programming Formulation of the Boolean Satisfiability Problem | Theorem 38 and Corollary 39 are in error. The modeling needs 9-dimensional z-variables instead of the 8-dimensional variables defined in notations 24.1. Examples of the correct model (with 9-index variables) are: (1) Diaby, M., "Linear Programming Formulation of the Set Partitioning Problem," International Journal of Operational Research 8:4 (August 2010) pp. 399-427; (2) Diaby, M., "Linear Programming Formulation of the Vertex Coloring Problem," International Journal of Mathematics in Operational Research 2:3 (May 2010) pp. 259-289; (3) Diaby, M., "The Traveling Salesman Problem: A Linear Programming Formulation," WSEAS Transactions on Mathematics, 6:6 (June 2007) pp. 745-754. | Discrete Mathematics (cs.DM) | 30 pages; 4 figures; Minor terminology clarification (Definition 4) | typos in manuscript | 231 |
0808.3588v2 | Discrete Affine Surfaces based on Quadrangular Meshes | In this paper we are interested in defining affine structures on discrete quadrangular surfaces of the affine three-space. We introduce, in a constructive way, two classes of such surfaces, called respectively indefinite and definite surfaces. The underlying meshes for indefinite surfaces are asymptotic nets satisfying a non-degeneracy condition, while the underlying meshes for definite surfaces are non-degenerate conjugate nets satisfying a certain natural condition. In both cases we associate to any of these nets several discrete affine invariant quantities: a metric, a normal and a co-normal vector fields, and a mean curvature. Moreover, we derive structural and compatibility equations which are shown to be necessary and sufficient conditions for the existence of a discrete quadrangular surface with a given affine structure. | Differential Geometry (math.DG) | The paper will be re-written in a different context | incomplete exposition or more work in progress | 232 |
0808.4120v2 | Magnetocapacitance of a graphene monolayer | We present a theoretical study of magnetocapacitance in a graphene monolayer at finite temperature taking into account the effects of disorder. The density of states (DOS) and magnetocapacitance found for graphene are compared to those found in standard two dimensional electron gas (2DEG) systems. The magnetic oscillations in DOS and magnetocapacitance are found to be enhanced and much more robust with respect to temperature damping in monolayer graphene in comparison with a 2DEG. Furthermore, we find that there is a $\pi$ phase shift between magnetic oscillations in the two systems which can be attributed to Dirac electrons in graphene acquiring a Berry's phase as they traverse a closed path in a magnetic field. | Mesoscale and Nanoscale Physics (cond-mat.mes-hall) | Withdrawn due to some changes in other paper; the paper has been withdrawn due to further changes in the manuscript | incomplete exposition or more work in progress | 233 |
0809.0073v3 | Languages recognized with unbounded error by quantum finite automata | This paper has been superseded by arXiv:1007.3624 | Quantum Physics (quant-ph) | This paper has been superseded by arXiv:1007.3624 | subsumed by another publication | 234 |
0809.0102v3 | Maxwell electromagnetic theory from a viewpoint of differential forms | In this paper, we discuss the Maxwell equations in terms of differential forms, both in the 3-dimensional space and in the 4-dimensional space-time manifold. Further, we view the classical electrodynamics as the curvature of a line bundle, and fit it into gauge theory. | Mathematical Physics (math-ph) | This paper has been withdrawn by the authors. withdrawn | reason not specified | 235 |
0809.0538v2 | Boolean Algebras and Logic | In this article we investigate the notion and basic properties of Boolean algebras and prove the Stone's representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof of completeness theorem in propositional logic will be given using Stone's theorem from Boolean algebra. | Logic (math.LO) | This paper has been withdrawn by the author. withdrawn | reason not specified | 236 |
0809.0540v2 | The nonmeasurability of Bernstein sets and related topics | In this article, we shall explore the constructions of Bernstein sets, and prove that every Bernstein set is nonmeasurable and doesn't have the property of Baire. We shall also prove that Bernstein sets don't have the perfect set property. | Classical Analysis and ODEs (math.CA) | This paper has been withdrawn by the author. withdrawn | reason not specified | 237 |
0809.0775v2 | Determining Seebeck coefficient of heavily doped La:SrTiO3 from density functional calculations | A new approach is developed to calculate temperature dependent Seebeck coefficient of heavily doped systems by using Boltzmann transport theory and electron density of states (DOS) obtained from density functional calculations. This approach is applied to heavily doped La:STO with DOS from tetrahedral method and Fermi energy using Fermi integrals. The calculated Seebeck coefficient agrees with the experimental data nearly quantitatively, which proved the accuracy of this approach. The influence of the Fermi energy and asymmetry of DOS on the Seebeck coefficient is analyzed. | Materials Science (cond-mat.mtrl-sci) | 19 pages, 4 figures | reason not specified | 238 |
0809.1276v6 | Matter Wave Radiation Leading to Matter Teleportation | The concept of matter wave radiation is put forward, and its equation is established for the first time. The formalism solution shows that the probability density is a function of displacement and time. A free particle and a two-level system are reinvestigated considering the effect of matter wave radiation. Three feasible experimental designs, especially a modified Stern-Gerlach setup, are proposed to verify the existence of matter wave radiation. Matter wave radiation effect in relativity has been formulated in only a raw formulae, which offers another explanation of Lamb shift. A possible mechanics of matter teleportation is predicted due to the effect of matter wave radiation. | General Physics (physics.gen-ph) | Like other waves e.g. electromagnetic wave, gravitational wave, de Broglie matter wave would have its wave source, is the source just Born probability density? It looks absurd. Three is no the room of the matter source in modern physics framework | factual/methodological/other critical errors in manuscript | 239 |
0809.1483v3 | Complete 3d-Homogeneous Manifolds | Assume that $M$ is close three dimensional manifold. We prove that $M\setminus \{p\}$ is a complete homogeneous manifold. As a corollary, we give a new proof on the classical Poincaré's conjecture. | General Mathematics (math.GM) | This paper contains a gap. This submission has been withdrawn by the author. | incomplete exposition or more work in progress | 240 |
0809.1719v4 | Duality in spaces of finite linear combinations of atoms | In this note we describe the dual and the completion of the space of finite linear combinations of $(p,\infty)$-atoms, $0<p\leq 1$ on ${\mathbb R}^n$. As an application, we show an extension result for operators uniformly bounded on $(p,\infty)$-atoms, $0<p < 1$, whose analogue for $p=1$ is known to be false. Let $0 < p <1$ and let $T$ be a linear operator defined on the space of finite linear combinations of $(p,\infty)$-atoms, $0<p < 1 $, which takes values in a Banach space $B$. If $T$ is uniformly bounded on $(p,\infty)$-atoms, then $T$ extends to a bounded operator from $H^p({\mathbb R}^n)$ into $B$. | Functional Analysis (math.FA) | The paper has appeared as Ricci, F., & Verdera, J. (2011). Duality in spaces of finite linear combinations of atoms. Transactions of the [REDACTED-NAME] Society, 363(3), 1311-1323 | subsumed by another publication | 241 |
0809.1754v2 | A note concerning a tidying procedure and contraction groups in non-metrizable, totally disconnected groups | In a 2004 article, Udo Baumgartner and George Willis used ideas from the structure theory of totally disconnected, locally compact groups to achieve a better understanding of the contraction group U_f associated with an automorphism f of such a group G, assuming that G is metrizable. (Recall that U_f consists of all group elements x such that f^n(x) tends to the identity element as n tends to infinity). Recently, Wojciech Jaworski showed that the main technical tool of the latter article remains valid in the non-metrizable case. He asserted without proof that, therefore, all results from that article remain valid. However, metrizability enters the arguments at a second point. In this note, we resolve this difficulty, by providing an affirmative answer to a question posed by Willis in 2004. | Group Theory (math.GR) | A superior, direct discussion of the "second point" mentioned in the abstract has been communicated by W. Jaworski to the author, which makes the reduction step to metrizable groups unnecessary. Therefore the note has been withdrawn | subsumed by another publication | 242 |
0809.2035v2 | Instability of Standing Waves to the Inhomogeneous Nonlinear Schrödinger Equation with Harmonic Potential | We study the instability of standing-wave solutions $e^{i\omega t}\phi_{\omega}(x)$ to the inhomogeneous nonlinear Schrödinger equation $$i\phi_t=-\triangle\phi+|x|^2\phi-|x|^b|\phi|^{p-1}\phi, \qquad \in\mathbb{R}^N, $$ where $ b > 0 $ and $ \phi_{\omega} $ is a ground-state solution. The results of the instability of standing-wave solutions reveal a balance between the frequency $\omega $ of wave and the power of nonlinearity $p $ for any fixed $ b > 0. $ | Analysis of PDEs (math.AP) | 21pages | reason not specified | 243 |
0809.2043v5 | Can the study of reduction probabilities reveal news about the nature of quantum state reduction? | A phenomenological model for the calculation of reduction probabilities of a superposition of several states is presented. The approach bases only the idea that quantum state reduction has its origin in a mutual physical interaction between the states. The model is explicitly worked out for the gravitational reduction hypothesis of Diosi and Penrose. It agrees for typical quantum mechanical experiments with the projection postulate and predicts regimes in which other behavior could be observed. An outlook is given, how the new effects can possibly become of interest for biology. For verification a feasible quantum optical experiment is proposed. The approach is analyzed from the view point of quantum non-locality in concrete its consequences for signalling. | Quantum Physics (quant-ph) | This publication has become obsolet due to four publications of the author in 2017. See arXiv:1701.01765, arXiv:1701.00343, arXiv:1701.00355 and arXiv:1701.00353) | subsumed by another publication | 244 |
0809.2135v3 | Extending Cantor Paradox | The inconsistencies involved in the foundation of set theory were invariably caused by infinity and self-reference; and only with the opportune axiomatic restrictions could them be obviated. Throughout history, both concepts have proved to be an exhaustible source of paradoxes and contradictions. It seems therefore legitimate to pose some questions concerning their formal consistency. This is just the objective of this paper. Starting from an extension of Cantor's paradox that suggests the inconsistency of the actual infinity, the paper makes a short review of its controversial history and proposes a new way of criticism based on w-order. Self-reference is also examined from a critique perspective which includes syntactic and semantic considerations. The critique affects the formal sentence involved in Godel's first incompleteness theorem and its ordinary language interpretation. | General Mathematics (math.GM) | Obsolete version | subsumed by another publication | 245 |
0809.2218v7 | A free action of a finite group on 3-sphere equivalent to a linear action | In this paper, by use of techniques associated to Cobordism theory and Morse theory, we give a proof of Space-Form-Conjecture, i.e. a free action of a finite group on 3-manifold is equivalent to a linear action. | Algebraic Topology (math.AT) | This paper has been withdrawn by the author | reason not specified | 246 |
0809.2252v3 | Unconditional security of continuous-variable quantum key distribution | The unconditional security of continuous-variable quantum key distribution is established for all schemes based on the estimation of the channel loss and excess noise. It is proved that, in the limit of large keys, Gaussian attacks are asymptotically optimal among the most general (coherent) attacks, where the transmission is tapped using arbitrary ancillas and stored in a quantum memory as a whole. Then, it is shown that the previously derived bounds on the achievable secret key rates against collective attacks remain asymptotically valid for arbitrary coherent attacks. | Quantum Physics (quant-ph) | This paper has been withdrawn by the authors. The approach investigated in this preprint fails for the following reason: for a fixed $n$, the $ε$-smooth min-entropy is a continuous function of $ε$ for a given $n$-mode state but the Lipschitz constant of the function increases with $n$. As a consequence, one cannot interchange the limits $ε$ tending to 0 with $n$ tending to infinity. Note, however, that an unconditional security proof of continuous-variable quantum key distribution was established in Phys. Rev. Lett. 102, 110504 (2009) (preprint arXiv:0809.2243) | factual/methodological/other critical errors in manuscript | 247 |
0809.2523v2 | Growth conditions and uniqueness of the Cauchy problem for the evolutionary infinity Laplacian | We study the Cauchy problem for the parabolic infinity Laplace equation. We prove a new comparison principle and obtain uniqueness of viscosity solutions in the class of functions with a polinomial growth at infinity, improving previous results obtained assuming a linear growth. | Analysis of PDEs (math.AP) | This paper has been withdrawn by the author due to a gap in the proof of Lemma 2.3. In fact, the condition $Φ(x,y,0,0) \leq 0$ does not directly follow from (6) and (7) | factual/methodological/other critical errors in manuscript | 248 |
0809.3105v4 | A Proof On Arnold-Chekanov Conjecture | In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations. | General Mathematics (math.GM) | This paper contains a gap. This submission has been withdrawn by the author. | incomplete exposition or more work in progress | 249 |
0809.3458v6 | A note on gaps | Let $p_{k}$ denote the $k$-th prime and $d(p_{k}) = p_{k} - p_{k - 1}$, the difference between consecutive primes. We denote by $N_{\epsilon}(x)$ the number of primes $\leq x$ which satisfy the inequality $d(p_{k}) \leq (\log p_{k})^{2 + \epsilon}$, where $\epsilon > 0$ is arbitrary and fixed, and by $\pi(x)$ the number of primes less than or equal to $x$. In this paper, we first prove a theorem that $\lim_{x \to \infty} N_{\epsilon}(x)/\pi(x) = 1$. A corollary to the proof of the theorem concerning gaps between consecutive squarefree numbers is stated. | General Mathematics (math.GM) | The paper should simply be forgotten, as it was pointed that this claim can be shown in three sentences | not novel | 251 |
0809.4309v2 | Deformation quantization modules II. Hochschild class | This paper is the continuation of arXiv:0802.1245 . We construct the Hochschild class for coherent modules over a deformation quantization algebroid on a complex Poisson manifold. We also define the convolution of Hochschild homologies, and prove that the Hochschild class of the convolution of two coherent modules is the convolution of their Hochschild classes. We study with some details the case of symplectic deformations. | Algebraic Geometry (math.AG) | The contents of this paper is now included in Deformation quantization modules (arXiv:1003.3304). | subsumed by another publication | 252 |
0809.4699v3 | Deformation of Sasakian metrics | We study the stability properties of Sasakian metrics in deformation theory. Let $\{F^{t}\}_{t \in T}$ be a smooth family of 1-dimensional transversely holomorphic Riemannian foliation on a closed manifold $M$, where $T$ is an open neighborhood of 0 in the L-dimensional Euclidean space and $F^{0}$ has a compatible Sasakian metric $g$. We give a necessary and sufficient condition under which there exist an open neighborhood $U$ of 0 in $T$ and a smooth family of Riemannian metric $\{g^{t}\}_{t \in U}$ on $M$ such that $g^{t}$ is a compatible Sasakian metric with $F^{t}$ for every $t$ in $U$ and $g^{0}=g$ in terms of the basic Euler classes of 1-dimensional isometric Riemannian foliations. As a corollary, we obtain a result on stability of Sasakian metrics of which the basic (0,2) Dolbeault number is zero in a family of 1-dimensional transversely holomorphic Riemannian foliation on $M$. | Differential Geometry (math.DG) | This paper has been withdrawn by the author due to a crucial error in the argument in the last paragraph of the proof of Lemma 6 | factual/methodological/other critical errors in manuscript | 253 |
0809.4781v2 | On contingent claims pricing in incomplete markets: A risk sharing approach | In an incomplete market setting, we consider two financial agents, who wish to price and trade a non-replicable contingent claim. Assuming that the agents are utility maximizers, we propose a transaction price which is a result of the minimization of a convex combination of their utility differences. We call this price the risk sharing price, we prove its existence for a large family of utility functions and we state some of its properties. As an example, we analyze extensively the case where both agents report exponential utility. | Computational Finance (q-fin.CP) | This paper has been withdrawn by the author since its revised version includes several modifications | incomplete exposition or more work in progress | 254 |
0809.5043v5 | On the particle production threshold for ultra-relativistic accelerated protons | Non-electromagnetic emission from cosmic ray particles accelerated in extreme environments has been studied using different variations of semi-classical formalisms. As the energy loss mechanisms of such particles is of great interest, one must improve in some sense the previously intuitive description of classical sources in the presence of fields. In this brief note we evaluate the role played by the classical and dimensional proper acceleration of a particle in radiation processes. One intends to show that the introduction of the acceleration as a measure parameter gives an adequate scale for considering the processes of massive particle emission. If the acceleration threshold is not attained one is considering a regime where the processes of massive particle production are suppressed. The analysis is performed in a semiclassical formalism once applied in different contexts and already checked for consistency in a serie of papers. As a further application of the results we evaluate the possibility of a non negligible meson production by protons accelerated in the framework of polar cap models operating in electromagnetic fields of pulsars. It is shown that inside a systems endowed with magnetic fields B\geq 10^{12} G the meson emission by protons must not be disregarded | High Energy Physics - Phenomenology (hep-ph) | Replaced. Improved discussion | incomplete exposition or more work in progress | 255 |
0810.0169v2 | Qualitative explanation of the temperature behaviors of the transport properties and magnetic susceptibility of high-temperature superconductors in the normal state | A model based on the alternating structure of the imbedded conduction layers (the Cu-O2 planes) with the charge-transfer-insulator (CTI) layers is proposed. There are three kinds of carriers, each with a different behavior: conduction-like holes in the Cu-O2 layers and electrons and normal holes in the CTI matrix between the Cu-O2 layers. This structure explains the strong anisotropies. The relationship is obtained between the concentration nq of conduction-like holes in the Cu-O2 layers and the temperature T. The anomalous temperature behavior of the resistivity as well as the Hall constant also follows. We give the hole density in ab plane a definite physical meaning, and also define explicitly optimal doping, overdoping and underdoping. Our model gives the correct temperature dependence of the resistivity and the hole constant on optimal doping, overdoping and underdoping, and it predicts the temperature behavior of the cotangent of the Hall angle quite well. Based on this model, we can also understand that the HiTc materials become "Fermi Liquids" in the extremely overdoped region, and the dR/dT becomes negative below some temperature T<1.211T0 in the underdoped case. Based on this model, the thermal behaviors of the magnetic susceptibility in different doping can also be easily explained. The resistivity along c-axis is discussed. | Superconductivity (cond-mat.supr-con) | 16 pages, 5 figures in one document | reason not specified | 256 |
0810.0558v2 | The Ratio Index for Budgeted Learning, with Applications | In the budgeted learning problem, we are allowed to experiment on a set of alternatives (given a fixed experimentation budget) with the goal of picking a single alternative with the largest possible expected payoff. Approximation algorithms for this problem were developed by Guha and Munagala by rounding a linear program that couples the various alternatives together. In this paper we present an index for this problem, which we call the ratio index, which also guarantees a constant factor approximation. Index-based policies have the advantage that a single number (i.e. the index) can be computed for each alternative irrespective of all other alternatives, and the alternative with the highest index is experimented upon. This is analogous to the famous Gittins index for the discounted multi-armed bandit problem. The ratio index has several interesting structural properties. First, we show that it can be computed in strongly polynomial time. Second, we show that with the appropriate discount factor, the Gittins index and our ratio index are constant factor approximations of each other, and hence the Gittins index also gives a constant factor approximation to the budgeted learning problem. Finally, we show that the ratio index can be used to create an index-based policy that achieves an O(1)-approximation for the finite horizon version of the multi-armed bandit problem. Moreover, the policy does not require any knowledge of the horizon (whereas we compare its performance against an optimal strategy that is aware of the horizon). This yields the following surprising result: there is an index-based policy that achieves an O(1)-approximation for the multi-armed bandit problem, oblivious to the underlying discount factor. | Data Structures and Algorithms (cs.DS) | This paper has a substantial bug that we are trying to fix. Many thanks to [REDACTED-NAME] for pointing this bug out. Please do not cite in the meantime. Please let us know if you would like to understand and/or try to fix the bug | factual/methodological/other critical errors in manuscript | 257 |
0810.0755v3 | DNA Bubble Life Time in Denaturation | We have investigated the denaturation bubble life time for a homogeneous as well as for a heterogeneous DNA within a Poland-Scheraga model. It is shown that at criticality the bubble life time for a homogeneous DNA is finite provided that the loop entropic exponent c>2 and has a scaling dependence on DNA length for c<2. Heterogeneity in the thermodynamical limit makes the bubble life time infinite for any entropic exponent. | Soft Condensed Matter (cond-mat.soft) | This paper has been withdrawn by the author due to mistakes | factual/methodological/other critical errors in manuscript | 258 |
0810.0805v2 | An Alternative Definition of the Completion of Metric Spaces | In this article, the author proposes another way to define the completion of a metric space, which is different from the classical one via the dense property, and prove the equivalence between two definitions. This definition is based on considerations from category theory, and can be generalized to arbitrary categories. | Functional Analysis (math.FA) | This paper has been withdrawn by the author. withdrawn | reason not specified | 259 |
0810.0881v2 | The structure of the exponent set for finite cyclic groups | We survey properties of the set of possible exponents of subsets of $\Z_n$ (equivalently, exponents of primitive circulant digraphs on $n$ vertices). Let $E_n$ denote this exponent set. We point out that $E_n$ contains the positive integers up to $\sqrt{n}$, the `large' exponents $\lfloor \frac{n}{3} \rfloor +1, \lfloor \frac{n}{2} \rfloor, n-1$, and for even $n \ge 4$, the additional value $\frac{n}{2}-1$. It is easy to see that no exponent in $[\frac{n}{2}+1,n-2]$ is possible, and Wang and Meng have shown that no exponent in $[\lfloor \frac{n}{3}\rfloor +2,\frac{n}{2}-2]$ is possible. Extending this result, we show that the interval $[\lfloor \frac{n}{4} \rfloor +3, \lfloor \frac{n}{3} \rfloor -2]$ is another gap in the exponent set $E_n$. In particular, $11 \not\in E_{35}$ and this gap is nonempty for all $n \ge 57$. A conjecture is made about further gaps in $E_n$ for large $n$. | Number Theory (math.NT) | This paper has been withdrawn since it's primary content is now subsumed by new work of the authors and [REDACTED-NAME] | subsumed by another publication | 260 |
0810.1937v6 | There are no $\mathcal{C}^5$-Regular Pure $y$-Global Landsberg Surfaces | We show that there are not pure $\mathcal{C}^5$ regular y-global Landsberg surfaced. The proof is based on the averaged connection associated with the linear Chern's connection and the classification of irreducibles holonomies of torsion-free affine connections. The structure consists on exausting all the possible cases and showing that in dimension 2 Landsberg condition implies Berwald condition. | Differential Geometry (math.DG) | This paper has been withdrawn by the author | reason not specified | 261 |
0810.2102v19 | Proof of the the Riemann hypothesis from the density and Lindelof hypotheses via a power sum method | The Riemann hypothesis is equivalent to the $\varpi$-form of the prime number theorem as $\varpi(x) =O(x\sp{1/2} \log\sp{2} x)$, where $\varpi(x) =\sum\sb{n\le x}\ \bigl(\Lambda(n) -1\big)$ with the sum running through the set of all natural integers. Let ${\mathsf Z}(s) = -\tfrac{\zeta\sp{\prime}(s)}{\zeta(s)} -\zeta(s)$. We use the classical integral formula for the Heaviside function in the form of ${\mathsf H}(x) =\int\sb{m -i\infty} \sp{m +i\infty} \tfrac{x\sp{s}}{s} \dd s$ where $m >0$, and ${\mathsf H}(x)$ is 0 when $\tfrac{1}{2} <x <1$, $\tfrac{1}{2}$ when $x=1$, and 1 when $x >1$. However, we diverge from the literature by applying Cauchy's residue theorem to the function ${\mathsf Z}(s) \cdot \tfrac{x\sp{s}} {s}$, rather than $-\tfrac{\zeta\sp{\prime}(s)} {\zeta(s)} \cdot \tfrac{x\sp{s}}{s}$, so that we may utilize the formula for $\tfrac{1}{2}< m <1$, under certain conditions. Starting with the estimate on $\varpi(x)$ from the trivial zero-free region $\sigma >1$ of ${\mathsf Z}(s)$, we use induction to reduce the size of the exponent $\theta$ in $\varpi(x) =O(x\sp{\theta} \log\sp{2} x)$, while we also use induction on $x$ when $\theta$ is fixed. We prove that the Riemann hypothesis is valid under the assumptions of the explicit strong density hypothesis and the Lindelöf hypothesis recently proven, via a result of the implication on the zero free regions from the remainder terms of the prime number theorem by the power sum method of Turán. | General Mathematics (math.GM) | This submission has been withdrawn by arXiv administrators due to disputed authorship | administrative or legal issues | 262 |
0810.2103v15 | Proof of the strong Density Hypothesis | The Riemann hypothesis, conjectured by Bernhard Riemann in 1859, claims that the non-trivial zeros of $\zeta(s)$ lie on the line $\Re(s) =1/2$. The density hypothesis is a conjectured estimate $N(\lambda, T) =O\bigl(T\sp{2(1-\lambda) +\epsilon} \bigr)$ for any $\epsilon >0$, where $N(\lambda, T)$ is the number of zeros of $\zeta(s)$ when $\Re(s) \ge\lambda$ and $0 <\Im(s) \le T$, with $1/2 \le \lambda \le 1$ and $T >0$. The Riemann-von Mangoldt Theorem confirms this estimate when $\lambda =1/2$, with $T\sp{\epsilon}$ being replaced by $\log T$. In an attempt to transform Backlund's proof of the Riemann-von Mangoldt Theorem to a proof of the density hypothesis by convexity, we discovered a different approach utilizing an auxiliary function. The crucial point is that this function should be devised to be symmetric with respect to $\Re(s) =1/2$ and about the size of the Euler Gamma function on the right hand side of the line $\Re(s) =1/2$. Moreover, it should be analytic and without any zeros in the concerned region. We indeed found such a function, which we call pseudo-Gamma function. With its help, we are able to establish a proof of the density hypothesis. Actually, we give the result explicitly and our result is even stronger than the original density hypothesis, namely it yields $N(\lambda, T) \le 8.734 \log T$ for any $1/2 < \lambda < 1$ and $T\ge 2445999554999$. | General Mathematics (math.GM) | This submission has been withdrawn by arXiv administrators due to disputed authorship | administrative or legal issues | 264 |
0810.2150v2 | A Model for Communication in Clusters of Multi-core Machines | A common paradigm for scientific computing is distributed message-passing systems, and a common approach to these systems is to implement them across clusters of high-performance workstations. As multi-core architectures become increasingly mainstream, these clusters are very likely to include multi-core machines. However, the theoretical models which are currently used to develop communication algorithms across these systems do not take into account the unique properties of processes running on shared-memory architectures, including shared external network connections and communication via shared memory locations. Because of this, existing algorithms are far from optimal for modern clusters. Additionally, recent attempts to adapt these algorithms to multicore systems have proceeded without the introduction of a more accurate formal model and have generally neglected to capitalize on the full power these systems offer. We propose a new model which simply and effectively captures the strengths of multi-core machines in collective communications patterns and suggest how it could be used to properly optimize these patterns. | Distributed, Parallel, and Cluster Computing (cs.DC) | This paper has been withdrawn by the author because it was basically a short-hand write-up of an incompletely formed idea from her Masters, and she'd like to start using her ArXiv account for her formal PhD research | incomplete exposition or more work in progress | 265 |
0810.2738v2 | Specific permutation polynomials over finite fields | We present new classes of permutation polynomials over finite fields. If $q$ is the order of a finite field, some polynomials are of form $x^r f(x^{(q-1)/d})$, where $d|(q-1)$. Other permutation polynomials are related with the trace function. | Number Theory (math.NT) | withdrawn by the author [preventing conflict of copyright] | administrative or legal issues | 266 |
0810.2970v5 | Large-time rescaling behaviors of some rational type solutions to the Polubarinova-Galin equation with injection | The main goal of this paper is to give a precise description of rescaling behaviors of rational type global strong solutions to the Polubarinova-Galin equation. The Polubarinova-Galin equation is the reformulation of the zero surface tension Hele-Shaw problem with a single source at the origin by considering the moving domain as the Riemann mapping of the unit disk centered at the origin. The coefficients $\{a_{k}(t)\}_{k\geq 2}$ of the polynomial strong solution $f_{k_{0}}(\xi,t)=\sum_{i=1}^{k_{0}}a_{i}(t)\xi^{i}$ decay to zero algebraically as $t^{-\lambda_{k}}$ ($\lambda_{k}=k/2$) and the decay is even faster if the low Richardson moments vanish. The dynamics for global solutions are discussed as well. | Mathematical Physics (math-ph) | This paper has been withdrawn by the author. 34 pages | reason not specified | 267 |
0810.2975v6 | Large-time rescaling behaviors for large data to the Hele-Shaw problem | This paper addresses a rescaling behavior of some classes of global solutions to the zero surface tension Hele-Shaw problem with injection at the origin, $\{\Omega(t)\}_{t\geq 0}$. Here $\Omega(0)$ is a small perturbation of $f(B_{1}(0),0)$ if $f(\xi,t)$ is a global strong polynomial solution to the Polubarinova-Galin equation with injection at the origin and we prove the solution $\Omega(t)$ is global as well. We rescale the domain $\Omega(t)$ so that the new domain $\Omega^{'}(t)$ always has area $\pi$ and we consider $\partial\Omega^{'}(t)$ as the radial perturbation of the unit circle centered at the origin for $t$ large enough. It is shown that the radial perturbation decays algebraically as $t^{-\lambda}$. This decay also implies that the curvature of $\partial\Omega^{'}(t)$ decays to 1 algebraically as $t^{-\lambda}$. The decay is faster if the low Richardson moments vanish. We also explain this work as the generalization of Vondenhoff's work which deals with the case that $f(\xi,t)=a_{1}(t)\xi$. | Mathematical Physics (math-ph) | This submission has been withdrawn by the author. 27 pages, 1 figure | reason not specified | 268 |
0810.2979v5 | Existence and uniqueness of the Hele-Shaw problem with injection | This paper gives a new and short proof of existence and uniqueness of the Polubarinova-Galin equation. The existence proof is an application of the main theorem in Lin's paper. Furthermore, we can conclude that every strong solution can be approximated by many strong polynomial solutions locally in time. | Mathematical Physics (math-ph) | This submission has been withdrawn by the author. 9 pages | reason not specified | 269 |
0810.3121v2 | Asymptotic normality for deconvolution kernel density estimators from random fields | The paper discusses the estimation of a continuous density function of the target random field $X_{\bf{i}}$, $\bf{i}\in \mathbb {Z}^N$ which is contaminated by measurement errors. In particular, the observed random field $Y_{\bf{i}}$, $\bf{i}\in \mathbb {Z}^N$ is such that $Y_{\bf{i}}=X_{\bf{i}}+\epsilon_{\bf{i}}$, where the random error $\epsilon_{\bf{i}}$ is from a known distribution and independent of the target random field. Compared to the existing results, the paper is improved in two directions. First, the random vectors in contrast to univariate random variables are investigated. Second, a random field with a certain spatial interactions instead of i. i. d. random variables is studied. Asymptotic normality of the proposed estimator is established under appropriate conditions. | Statistics Theory (math.ST) | This paper need significant enhancement. After necessary enhancement, the paper will be submitted to a journal for publication! | incomplete exposition or more work in progress | 270 |
0810.3287v2 | WTC solutions to a generalized nonlinear Schrödinger equation | A generalized nonlinear Schrödinger equation admits WTC formal solutions as was shown by Clarkson. We show that they are convergent and determine real-analytic solutions near a noncharacteristic, movable singularity manifold. | Analysis of PDEs (math.AP) | This paper has been withdrawn since the author now thinks it needs much improvement | incomplete exposition or more work in progress | 271 |
0810.3729v2 | Optimal codes in deletion and insertion metric | We improve the upper bound of Levenshtein for the cardinality of a code of length 4 capable of correcting single deletions over an alphabet of even size. We also illustrate that the new upper bound is sharp. Furthermore we will construct an optimal perfect code capable of correcting single deletions for the same parameters. | Information Theory (cs.IT) | 19 pages,The material of this paper was presented in part at the 10th [REDACTED-NAME] on Algebraic and [REDACTED-NAME] Theory, Zvenigorod, Russia, September 2006 | subsumed by another publication | 272 |
0810.3972v2 | A History of Solar Activity over Millennia | Presented here is a review of present knowledge of the long-term behavior of solar activity on a multi-millennial timescale, as reconstructed using the indirect proxy method. The concept of solar activity is discussed along with an overview of the special indices used to quantify different aspects of variable solar activity, with special emphasis upon sunspot number. Over long timescales, quantitative information about past solar activity can only be obtained using a method based upon indirect proxy, such as the cosmogenic isotopes 14C and 10Be in natural stratified archives (e.g., tree rings or ice cores). We give an historical overview of the development of the proxy-based method for past solar-activity reconstruction over millennia, as well as a description of the modern state. Special attention is paid to the verification and cross-calibration of reconstructions. It is argued that this method of cosmogenic isotopes makes a solid basis for studies of solar variability in the past on a long timescale (centuries to millennia) during the Holocene. A separate section is devoted to reconstructions of strong solar energetic particle (SEP) events in the past, that suggest that the present-day average SEP flux is broadly consistent with estimates on longer timescales, and that the occurrence of extra-strong events is unlikely. Finally, the main features of the long-term evolution of solar magnetic activity, including the statistics of grand minima and maxima occurrence, are summarized and their possible implications, especially for solar/stellar dynamo theory, are discussed. | Astrophysics (astro-ph) | This paper has been withdrawn by the author because of the new review published in [REDACTED-NAME] in [REDACTED-NAME] <this http URL | subsumed by another publication | 273 |
0810.5335v3 | The Algorithmic Behaviour of the F5 Algorithm | This paper has been withdrawn due to an error in the proof of the termination of the algorithm. Moreover, some ideas of this paper are a joint work with John Perry and it is inappropriate to mention only me as an author. John Perry was in spite of the statement in the acknowledgment of previous versions not proofreading this paper.
Recently we have found a new solution for ensuring F5's termination, which can be found here : arXiv:1006.0318 . | Commutative Algebra (math.AC) | This paper has been withdrawn | reason not specified | 274 |
0810.5349v2 | Monte Carlo discretization of general relativistic radiation transport | An indirect, hybrid Monte Carlo discretization of general relativistic kinetic theory suitable for the development of numerical schemes for radiation transport is presented. The discretization is based on surface flux estimators obtained from a local decomposition of the distribution function, and can handle optically thick regions by means of formal solutions within each cell. Furthermore, the scheme is designed for parallel implementation, and it admits the use of adaptive techniques by virtue of leaving all probability density functions unspecified. Some considerations for numerical uses of the scheme are discussed. | Astrophysics (astro-ph) | This paper describes a discretization method for general relativistic radiation transport. I now consider it incomplete in that it has no supporting numerical evidence inside the publication, and I have decided to withdraw the paper until I find the time to provide such evidence | incomplete exposition or more work in progress | 275 |
0810.5610v2 | The BCS Gap Equation on a Banach Space Consisting of Functions both of the Temperature and of the Wave Vector | In previous mathematical studies of the BCS gap equation of superconductivity, the gap function was regarded as an element of a space consisting of functions of the wave vector only. But we regard it as an element of a Banach space consisting of functions both of the temperature and of the wave vector. On the basis of the implicit function theorem we first show that there is a unique solution of class $C^2$ with respect to the temperature, to the simplified gap equation obtained from the BCS gap equation. We then regard the BCS gap equation as a nonlinear integral equation on the Banach space above, and show that there is a unique solution to the BCS gap equation on the basis of the Schauder fixed-point theorem. We find that the solution to the BCS gap equation is continuous with respect to both the temperature and the wave vector, and that the solution is approximated by a function of class $C^2$ with respect to both the temperature and the wave vector. Moreover, the solution to the BCS gap equation is shown to reduce to the solution to the simplified gap equation under a certain condition. | Mathematical Physics (math-ph) | This paper has been withdrawn by the author due to an error in Lemma 4.5 | factual/methodological/other critical errors in manuscript | 276 |
0810.5629v2 | Simultaneous Binary Collisions for Collinear Four-Body Problem | In this paper, we use canonical transformations to collectively analytically continue the singularities of the simultaneous binary collision solutions for the collinear four- body problem in both the decoupled case and the coupled case. All the solutions are found and more importantly, we describe the relationship between the decoupled solutions and the coupled solutions. | Dynamical Systems (math.DS) | This paper has been withdrawn by the authors. no comments | reason not specified | 277 |
0811.0406v3 | Discrete multivariate distributions | This article brings in two new discrete distributions: multidimensional Binomial distribution and multidimensional Poisson distribution. Those distributions were created in eventology as more correct generalizations of Binomial and Poisson distributions. Accordingly to eventology new laws take into account full distribution of events. Also, in article its characteristics and properties are described | General Mathematics (math.GM) | This paper has been withdrawn by the authors | reason not specified | 278 |
0811.0420v3 | Eventological theory of decision making for stock markets | The eventological theory of decision-making, the theory of eventfull decision-making is a theory of decision-making based on eventological principles and using results of mathematical eventology; a theoretical basis of the practical eventology. The beginnings of this theory which have arisen from eventfull representation of the reasonable subject and his decisions in the form of eventological distributions (E-distributions) of sets of events and which are based on the eventological H-theorem are offered. The illustrative example of the eventological decision-making by the reasonable subject on his own eventfull behaviour in the financial or share market is considered. | General Mathematics (math.GM) | This paper has been withdrawn by the authors | reason not specified | 279 |
0811.0430v2 | An Analysis of the Bias-Property of the Sample Auto-Correlation Matrices of Doubly Selective Fading Channels for OFDM Systems | This paper derives the analytic expression of the sample auto-correlation matrix from the least-squared channel estimation of doubly selective fading channels for OFDM systems. According to the expression, the sample auto-correlation matrix reveals the bias property which would cause the model mismatch and therefore deteriorate the performance of channel estimation. Numerical results demonstrate the bias property and corresponding analysis. | Information Theory (cs.IT) | not sufficiently novel | not novel | 280 |
0811.0505v2 | Sharp ill-posedness result for the periodic Benjamin-Ono equation | We prove the discontinuity for the weak $ L^2(\T) $-topology of the flow-map associated with the periodic Benjamin-Ono equation. This ensures that this equation is ill-posed in $ H^s(\T) $ as soon as $ s<0 $ and thus completes exactly the well-posedness result obtained by the author. | Analysis of PDEs (math.AP) | This paper has been withdrawn by the author since there were errors in the calculus of the defect coefficient in Page 11. The corrected calculus gives actually zero which do not lead to a contradiction on the continuity of the flow-map of the Benjamin-Ono equation. The author warmly thank [REDACTED-NAME] Gérard for having pointing out this error to him | factual/methodological/other critical errors in manuscript | 281 |
0811.0548v2 | On $ω_3$-chains in P($ω_1$) mod finite | We prove that if there exists a simplified $(\omega_1,2)$-morass, then there is a ccc forcing which adds an $\omega_3$-chain in P($\omega_1$) mod finite and a ccc forcing which adds a family of $\omega_3$-many strongly almost disjoint functions from $\omega_1$ to $\omega$. The idea is to use a finite support iteration of countable forcings which is not linear but three-dimensional. | Logic (math.LO) | There are some gaps in the proof which I am unable to fix | incomplete exposition or more work in progress | 282 |
0811.0935v5 | A New Training Protocol for Channel State Estimation in Wireless Relay Networks | The accuracy of channel state information (CSI) is critical for improving the capacity of wireless networks. In this paper, we introduce a training protocol for wireless relay networks that uses channel estimation and feedforwarding methods. The feedforwarding method is the distinctive feature of the proposed protocol. As we show, each relay feedforwards the imperfect CSI to the destination in a way that provides a higher network capacity and a faster transfer of the CSI than the existing protocols. In addition, we show the importance of the effective CSI accuracy on the wireless relay network capacity by comparing networks with the perfect effective CSI, imperfect effective CSI, and noisy imperfect effective CSI available at the destination. | Information Theory (cs.IT) | This paper has been withdrawn by the author due to technical flaws in SISO section | factual/methodological/other critical errors in manuscript | 283 |
0811.1360v2 | On complex positive definite functions on Z_n vanishing on squares | We generalize the Sarkozy-Furstenberg theorem on squares in difference sets of integers, and show that, given any positive definite function f:Z_N->C with density at least r(N), where r(N)=O((\log N)^{-c}), there is a perfect square s<=N/2 such that f(s) is non-zero. We do not rely on the usual analysis of the dichotomy of randomness and periodicity of a set and iterative application of the Hardy-Littlewood method. Instead, we find a bound for the van der Corput property of the set of squares. | Number Theory (math.NT) | The paper has been completely revised and posted in a new form and with a new title, as accepted for publishing | subsumed by another publication | 284 |
0811.1948v3 | Exact solutions in the Dirac-Born-Infeld effective theory and the fate of tachyon | We show that the equation of motion from the Dirac-Born-Infeld effective action of a general scalar field with some specific potentials admits exact solutions after appropriate field redefinitions. Based on the exact solutions and their energy-momentum tensors, we find that massive scalars and massless scalars of oscillating modes in the DBI effective theory are not pressureless generically for any possible momenta, which implies that the pressureless "tachyon matter" forming at late time of the tachyon condensation process should not really be some massive matter. It is more likely that the tachyon field at late time behaves as a massless scalar of zero modes. At kinks, the tachyon can be viewed as a massless scalar of a translational zero mode describing a stable and static D-brane with one dimension lower. Near the vacuum, the tachyon in regions without the caustic singularities can be viewed as a massless scalar that has the same zero mode solution as a fundamental string moving with a critical velocity. We find supporting evidences to this conclusion by considering a DBI theory with modified tachyon potential, in which the development of caustics near the vacuum may be avoided. | High Energy Physics - Theory (hep-th) | contains no significant results | not novel | 285 |
0811.2080v2 | Axiomatic framework for the BGG Category O | The main goal of this paper is to show that a wide variety of infinite-dimensional algebras all share a common structure, including a triangular decomposition and a theory of weights. This structure allows us to define and study the BGG Category O, generalizing previous definitions of it.
Having presented our axiomatic framework, we present sufficient conditions that guarantee finite length, enough projectives, and a block decomposition into highest weight categories. The framework is strictly more general than the usual theory of O; this is needed to accommodate (quantized or higher rank) infinitesimal Hecke algebras, in addition to semisimple Lie algebras and their quantum groups.
We then present numerous examples, two families of which are studied in detail. These are quantum groups defined using not necessarily the root or weight lattices (for these, we study the center and central characters), and infinitesimal Hecke algebras. | Representation Theory (math.RT) | This paper has been withdrawn by the author; see arXiv:1502.06706 which supersedes this paper, has been completely rewritten, and goes much further | subsumed by another publication | 286 |
0811.2430v4 | What particles that never met "know" of one another? | An experiment proposed by Yurke and Stoler, and similar to that realized experimentally by Sciarrino et al., is analyzed. In Sciarrino's realization, identical photons from a degenerated down-conversion pair are used, i.e. the photons met in the past. In the experiment analyzed here the particles are also identical, but from different sources. As long as one can tell from which source came each particle, the joint wave function remains factorizable. However, a configuration is created in which one cannot tell anymore which particle came from which source. As a result, the wave function becomes non-factorizable, symmetrical (for bosons) or antisymmetrical (for fermions). In part of the cases the situation is even more surprising: the particles never meet, s.t. the symmetry (antisymmetry) is produced at-a-distance without the particles having had the possibility to interact in any way. | Quantum Physics (quant-ph) | The author revised the article and considers that the proof is not rigorous. The main counter-argument is that one should not draw conclusions from a truncated wave-function | factual/methodological/other critical errors in manuscript | 287 |
0811.2543v2 | A Non-Renormalized Field Theoretic Treatment of Photon Scattering | In this paper we have presented a generalized treatment of a photon scattering by a harmonic oscillator initially at ground state. We have predicted the scattering cross-section of the oscillator and showed how the treatment invariably requires the formalisms of renormalization. As a special case of our treatment, we discussed about Rayleigh and Thomson Scattering and computed the total cross-section in order to be consistent with experimental results. Two approximations are adopted in order to simplify the problem but without any digression from our goal. A second order perturbation theory is employed where the first excited state of the harmonic oscillator is considered to be the only intermediate state and A dipole approximation is utilized. Throughout this paper we have used Gaussian units. | Quantum Physics (quant-ph) | NA | classification_error | 288 |
0811.2860v3 | Tropical rational equivalence on R^r | We introduce an improved version of rational equivalence in tropical intersection theory which can be seen as a replacement of chapter 8 of our previous article arXiv:0709.3705v2 . Using this new definition, rational equivalence is compatible with push-forwards of cycles. Moreover, we prove that every tropical cycle in R^r is equivalent to a uniquely determined affine cycle, called its degree. | Algebraic Geometry (math.AG) | 6 pages, 2 figures; minor fixes in version 2 This paper has been withdrawn. An updated and extended version (with a third author) is available here: arXiv:1408.1537 | subsumed by another publication | 289 |
0811.3427v2 | ADI finite difference schemes for option pricing in the Heston model with correlation | This paper deals with the numerical solution of the Heston partial differential equation that plays an important role in financial option pricing, Heston (1993, Rev. Finan. Stud. 6). A feature of this time-dependent, two-dimensional convection-diffusion-reaction equation is the presence of a mixed spatial-derivative term, which stems from the correlation between the two underlying stochastic processes for the asset price and its variance. Semi-discretization of the Heston PDE, using finite difference schemes on a non-uniform grid, gives rise to large systems of stiff ordinary differential equations. For the effective numerical solution of these systems, standard implicit time-stepping methods are often not suitable anymore, and tailored time-discretization methods are required. In the present paper, we investigate four splitting schemes of the Alternating Direction Implicit (ADI) type: the Douglas scheme, the Craig & Sneyd scheme, the Modified Craig & Sneyd scheme, and the Hundsdorfer & Verwer scheme - each of which contains a free parameter. ADI schemes were not originally developed to deal with mixed spatial-derivative terms. Accordingly, we first discuss the adaptation of the above four ADI schemes to the Heston equation. Subsequently, we present various numerical examples with realistic data sets from the literature, where we consider European call options as well as down-and-out barrier options. Combined with ample theoretical stability results for ADI schemes that have recently been obtained in In 't Hout & Welfert (2007, Appl. Numer. Math.), we arrive at three ADI schemes that all prove to be very effective in the numerical solution of the Heston PDE with a mixed derivative term. | Numerical Analysis (math.NA) | Paper has been published | subsumed by another publication | 290 |
0811.3431v2 | Operator Methods for the Time Evolution of Wave Functions | A method based off of operator consideration for solving the time evolution of a wave function is developed. The method is applied to free space, constant force and harmonic oscillator potentials where general solutions are derived for the wave function time evolutions for these potentials. Solving the Heisenberg equations of motion is discussed. A method to obtain exact solutions to Heisenberg's equations of motion is developed based off of solutions of classical equations of motion. Approximation methods for the time evolution of operators and wave functions are developed. A connection between classical and quantum chaos is made where it is realized that whenever a classical system behaves chaotically, the quantum system will as well. | Quantum Physics (quant-ph) | 18 pages; This paper has been withdrawn as it has not been parsed correctly | typos in manuscript | 291 |
0811.3485v2 | Soft-lubrication effect on the lateral migration of a slightly deformed bubble rising near a vertical plane wall | Deformation-induced lateral migration of a bubble slowly rising near a vertical plane wall in a stagnant liquid is numerically and theoretically investigated. In particular, our focus is set on a situation with a small clearance $c$ between the bubble interface and the wall. Motivated by the fact that experimentally measured migration velocity (Takemura et al. (2002, J. Fluid Mech. {\bf 461}, 277)) is higher than the velocity estimated by the available analytical solution (Magnaudet et al. (2003, J. Fluid Mech. {\bf 476}, 115)) using the Faxén mirror image technique for $\kappa(=a/(a+c))\ll 1$ (here $a$ is the bubble radius), when the clearance parameter $\epsilon(=c/a)$ is comparable to or smaller than unit, the numerical analysis based on the boundary-fitted finite-difference approach by solving the Stokes equation is performed to complement the experiment. To improve the understandings of a role of the squeezing flow within the bubble-wall gap, the theoretical analysis based on a soft-lubrication approach (Skotheim & Mahadevan (2004, Phys. Rev. Lett. {\bf 92}, 245509)) is also performed. The present analyses demonstrate the migration velocity scales $\propto{\rm Ca}\ \epsilon^{-1}V_{B1}$ (here, $V_{B1}$ and ${\rm Ca}$ denote the rising velocity and the capillary number, respectively) in the limit of $\epsilon\to 0$. | Fluid Dynamics (physics.flu-dyn) | This paper has been withdrawn by the author | reason not specified | 292 |
0811.4148v3 | Monoidal transformations of singularities in positive characteristic | A sequence of monoidal transformations is defined, in terms of invariants, for a singular hypersurface embedded in a smooth scheme of positive characteristic. Some examples are added to illustrate the improvement of singularities by this procedure. | Algebraic Geometry (math.AG) | This paper has been withdrawn by the authors due to most results are included in a current version which appears in arXiv:1004.1803 with a minor change of the title | subsumed by another publication | 293 |
0811.4613v2 | Pricing financial derivatives by a minimizing method | We shall study backward stochastic differential equations and we will present a new approach for the existence of the solution. This type of equation appears very often in the valuation of financial derivatives in complete markets. Therefore, the identification of the solution as the unique element in a certain Banach space where a suitably chosen functional attains its minimum becomes interesting for numerical computations. | Optimization and Control (math.OC) | This paper has been withdrawn by the author | reason not specified | 294 |
0812.0565v2 | Time turns the universal kaleidoscope | This (withdrawn) creative essay intended to consider the appearance of time's arrow in a fully symmetric universe compatible with "pilot wave" or transactional interpretations (D. Bohm or J.G. Kramer, respectively). The (unstated) hypothesis was that, despite unitary time evolution, the inherent Hilbert transform operator found in the energy operator of the Schrodinger equation and in commutation relations of Fourier observables indicates dissipation and seemingly, entropy increase. | Popular Physics (physics.pop-ph) | This article has been withdrawn by the author because it is inaccurate and unfinished | incomplete exposition or more work in progress | 295 |
0812.0634v2 | A multipixel silicon APD with ultralow dark count rate at liquid nitrogen temperature | The dark count rate of a multipixel photon counter (MPPC) was reduced to less than 0.2 cps by cooling the counter to 78.5 K. Characteristics of the MPPC other than the dark count rate were also detemined at 78.5 K and 295 K. The photodetection efficiency and the timing jitter at 78.5 K were comparable to those at 295 K. The MPPC had a count rate of up to 50 MHz at 78.5 K and above 100 MHz at 295 K. Detailed measurements were performed for detemining the afterpulse probability. | Quantum Physics (quant-ph) | 10 pages, 11 figures, 2 tables | reason not specified | 296 |
0812.0877v2 | Two-Parameter Heavy-Traffic Limits for Infinite-Server Queues | In order to obtain Markov heavy-traffic approximations for infinite-server queues with general non-exponential service-time distributions and general arrival processes, possibly with time-varying arrival rates, we establish heavy-traffic limits for two-parameter stochastic processes. We consider the random variables $Q^e(t,y)$ and $Q^r(t,y)$ representing the number of customers in the system at time $t$ that have elapsed service times less than or equal to time $y$, or residual service times strictly greater than $y$. We also consider $W^r(t,y)$ representing the total amount of work in service time remaining to be done at time $t+y$ for customers in the system at time $t$. The two-parameter stochastic-process limits in the space $D([0,\infty),D)$ of $D$-valued functions in $D$ draw on, and extend, previous heavy-traffic limits by Glynn and Whitt (1991), where the case of discrete service-time distributions was treated, and Krichagina and Puhalskii (1997), where it was shown that the variability of service times is captured by the Kiefer process with second argument set equal to the service-time c.d.f. | Probability (math.PR) | We want to withdraw this article because of a mistake in the proof and replace it with a new version | factual/methodological/other critical errors in manuscript | 297 |
0812.0885v2 | Elementary epistemological features of machine intelligence | Theoretical analysis of machine intelligence (MI) is useful for defining a common platform in both theoretical and applied artificial intelligence (AI). The goal of this paper is to set canonical definitions that can assist pragmatic research in both strong and weak AI. Described epistemological features of machine intelligence include relationship between intelligent behavior, intelligent and unintelligent machine characteristics, observable and unobservable entities and classification of intelligence. The paper also establishes algebraic definitions of efficiency and accuracy of MI tests as their quality measure. The last part of the paper addresses the learning process with respect to the traditional epistemology and the epistemology of MI described here. The proposed views on MI positively correlate to the Hegelian monistic epistemology and contribute towards amalgamating idealistic deliberations with the AI theory, particularly in a local frame of reference. | Artificial Intelligence (cs.AI) | The paper needs to be redesigned | incomplete exposition or more work in progress | 298 |
0812.0967v2 | Secret Broadcasting of GHZ type state | Here we described a protocol by which one can broadcast GHZ-type states secretly. We have done this with the help of a cloning machine followed by subsequent measurements. We also made a comparative study of the amount of residual tangle present in these entangled states, obtained as outputs of the measurements. | Quantum Physics (quant-ph) | This paper is withdrawn, as because the results are incorrect | factual/methodological/other critical errors in manuscript | 299 |
0812.1454v3 | Solymosi's multiplicative energy bound for complex numbers | We extend the recent Solymosi's sum-product estimate for reals to the complex case. | Combinatorics (math.CO) | This paper has been withdrawn by the authors. This paper has a fatal error. Many thanks to L. Li who pointed it out | factual/methodological/other critical errors in manuscript | 300 |
0812.1659v3 | Transport diffusion coefficient for a Knudsen gas in a random tube | We consider transport diffusion in a stochastic billiard in a random tube which is elongated in the direction of the first coordinate (the tube axis). Inside the random tube, which is stationary and ergodic, non-interacting particles move straight with constant speed. Upon hitting the tube walls, they are reflected randomly, according to the cosine law: the density of the outgoing direction is proportional to the cosine of the angle between this direction and the normal vector. Steady state transport is studied by introducing an open tube segment as follows: We cut out a large finite segment of the tube with segment boundaries perpendicular to the tube axis. Particles which leave this piece through the segment boundaries disappear from the system. Through stationary injection of particles at one boundary of the segment a steady state with non-vanishing stationary particle current is maintained. We prove (i) that in the thermodynamic limit of an infinite open piece the coarse-grained density profile inside the segment is linear, and (ii) that the transport diffusion coefficient obtained from the ratio of stationary current and effective boundary density gradient equals the diffusion coefficient of a tagged particle in an infinite tube. Thus we prove Fick's law and equality of transport diffusion and self-diffusion coefficients for quite generic rough (random) tubes. | Probability (math.PR) | This paper will not be published, since it contains a serious flaw in eq.(25). See http://arxiv.org/abs/1004.1206 for a corrected and extended version. | factual/methodological/other critical errors in manuscript | 301 |
0812.2160v2 | Minimally doubled chiral fermions with C, P and T symmetry on the staggered lattice | Recently, the interest in local lattice actions for chiral fermions has revived, with the proposition of new local actions in which only the minimal number of doublers appear. The trigger role of graphene having a minimally doubled, chirally invariant, Dirac-like excitation spectrum can not be neglected. The challenge is to construct an action which preserves enough symmetries to be useful in lattice gauge calculations. We present a new approach to obtain local lattice actions for fermions using a reinterpretation of the staggered lattice approach of Kogut and Susskind. This interpretation is based on the similarity with the staggered lattice approach in FDTD simulations of acoustics and electromagnetism. It allows us to construct a local action for chiral fermions which has all discrete symmetries and the minimal number of fermion flavors, but which is non-Hermitian in real space. However, we argue that this will not pose a threat to the usability of the theory. | High Energy Physics - Lattice (hep-lat) | Withdrawn due to the fact that it the proposed approach is restricted to discrete chiral symmetry and not easily generalizable to continuous chiral symmetry | incomplete exposition or more work in progress | 302 |
0812.2301v3 | Cooperative Hybrid ARQ Protocols: Unified Frameworks for Protocol Analysis | Cooperative hybrid-ARQ (HARQ) protocols, which can exploit the spatial and temporal diversities, have been widely studied. The efficiency of cooperative HARQ protocols is higher than that of cooperative protocols, because retransmissions are only performed when necessary. We classify cooperative HARQ protocols as three decode-and-forward based HARQ (DF-HARQ) protocols and two amplified-and-forward based (AF-HARQ) protocols. To compare these protocols and obtain the optimum parameters, two unified frameworks are developed for protocol analysis. Using the frameworks, we can evaluate and compare the maximum throughput and outage probabilities according to the SNR, the relay location, and the delay constraint for the protocols. | Information Theory (cs.IT) | This paper has been withdrawn by the author for submission to another journal | administrative or legal issues | 303 |
0812.2735v2 | The Cauchy-Crofton formula and the Whitney arc property for definable sets | We use the Cauchy-Crofton formula to show that every definable cell (bounded by a ball with rational radius) in an O-minimal expansion of a field extension of the real numbers satisfies the Whitney arc property. | Logic (math.LO) | 8 pages, This paper has been withdrawn by the author. The third sentence of the proof of Theorem 5.6 contained an error; the results are subsumed and extended by the paper "Hausdorff measure on o-minimal structures" with A. Fornasiero | subsumed by another publication | 304 |
0812.2753v2 | Note on the Fenchel transform in the Heisenberg group | Given a real-valued function defined on the Heisenberg group, we provide a definition of abstract convexity and Fenchel transform that takes into account the sub-Riemannian structure of the group. In our main result, we prove that, likewise the Euclidean case, a convex function can be characterized via its iterated Fenchel transform; the properties of the H-subdifferential play a crucial role. | Functional Analysis (math.FA) | The paper appeared in Journal of [REDACTED-NAME] and Applications, volume 368, issue 1, August 2010, pages 69-79. | subsumed by another publication | 305 |
0812.3699v2 | Multi-color Randomly Reinforced Urn for Adaptive Designs | This paper is withdrawn | Methodology (stat.ME) | 60F15 | reason not specified | 306 |
0812.3754v3 | Semiring Properties of Heyting Algebras | The relationship between Heyting algebras (HA) and semirings is explored. A new class of HAs called Symmetric Heyting algebras (SHAs) is proposed, and a necessary condition on SHAs to be consider semirings is given. We define a new mathematical family called Heyting structures, which are similar to semirings, but with Heyting-algebra operators in place of the usual arithmetic operators usually seen in semirings. The impact of the zero-sum free property of semirings on Heyting structures is shown as also the condition under which it is possible to extend one Heyting structure to another. It is also shown that the union of two or more sets forming Heyting structures is again a Heyting structure, if the operators on the new structure are suitably derived from those of the component structures. The analysis also provides a sufficient condition such that the larger Heyting structure satisfying a monotony law implies that the ones forming the union do so as well. | Rings and Algebras (math.RA) | The paper is withdrawn due to multiple errors that have been pointed to us by referees. | factual/methodological/other critical errors in manuscript | 307 |
0812.4009v20 | Graph Field Automata | The Graph Automata have been the paradigm in the expression of utilizing Graphs as a language. Matrix Graph grammars \cite{Pedro} are an algebratization of graph rewriting systems. Here we present the dual of this formalizm which some extensions which we term Graph Field Automata The advantage to this approach is a framework for expressing machines that can use Matrix Graph Grammars. | Computational Complexity (cs.CC) | 8 pages 1 figure v1 initial submission v2 [REDACTED-NAME] v3 More minor changes v4 still more minor changes v5 Rewritten base assumptions, more english corrections and minor changes v6 Major english corrections v7 Rewritten most of the paper. This paper doesn't make any sense | factual/methodological/other critical errors in manuscript | 308 |
Subsets and Splits