 are Black Hole mass equivalents defined in a Mass-Temperature (MT) Modulus and as first espoused by Stephen Hawking.
Applying the Schwarzschild metric to any particle carrying inertia will give a Schwarzschild radius much smaller than the superstring limit of 1.6x10-23 meters.
A proton of restmass 1.7x10-27 kg for example has a Schwarzschild radius of 4.2x10-54 meters and smaller than the Planck-Length limit of about 2x10-35 meters by 19 magnitudes.
The Hawking Modulus is MT=constant=9.4x1023 (kg.K) showing that the bigger a Black Hole is, the colder ist must be thermodynamically.
Subsequently the micro Black Hole energy equivalents are very hot using the Boltzmann quantum law E=kT in conjunction with Planck's E=hf and Einstein's E=mc2.
It are those 'Planck-scale busting' elementary particles and AS Black Hole string equivalents, which must appear in subatomic particle'smashers'.
As an inertial particle accelerates it becomes 'heavier' by the Energy-Momentum relation of Special Relativity and it is this increase in mass, which can be used to 'discover' new physics and elementary properties of fundamental particles as an excess energy following collision.
As the protons in the LHC move at over 99.99999% of lightspeed, their restmass is increased to over 1/√(1-.9999999892)~7,000 times their restmass.
Upon collision, this excess mass transforms as kinetic energy into the manifesting inertia of other elementary particles and associated couplings with respect to quark- and leptonic content configurations.
This energy transformation 'taps' the socalled vacuum energy of the 'virtual Heisenberg matrix', defined in elementary matter-antimatter or quark-antiquark or lepton-antilepton backgrounds.
The Higgs Boson accomodates all those backdrops as a quarkian up-down-strange double template. This is manifested at the low energy scale as a scalar squared (or doubled) lambda hyperon of quark content (uds)2.
As the LHC collides protons with protons, travelling in opposite directions, the debris products will be rather more messy, then if protons were to annihilate with antiprotons in the vacuum-characteristic quark-antiquark couplings.
In particular, the decomposition of a scalar double-lambda in terms of elementary particle families will 'tap' the vacuum potential energy as Vortex-Potential-Energy (VPE) in'resurrecting' the basic proton-proton core as a'squared' (udu)2, supplemented with the kinetic energy transformed via the VPE in mesonic quark-antiquark couplings depicting the 'proton differential' in terms of the quantum geometry of the Higgs Boson's encompassing master template.
As a down-quark consists of a mesonic inner ring coupled to an up-quark kernel and as the strange quark couples such an up-quark kernel to a leptonic outer ring; this quantum geometric difference will engage the quark-antiquark coupling strange-antistrange (s.sbar) as its fundamental resonance and so form the trajectories and pathways of the resulting debris of the proton beams, bounded by the energy realms under consideration.
The antimatter part derives from the vacuum VPE as mesonic quark-antiquark couplings and from this the u.ubar and d.dbar and s.sbar chains then combine to manifest particular elementary particle associations under the conservation laws of linear- and angular momenta and of energy.
As the combined interaction energy of the proton-proton collision is 14 TeV, the following table of diquark eigenstates is accomodated in principle and resonance'spikes' should appear at the indicated energy realms.
This table incorporates the Higgs Boson not as an individual particle, but as an encompassing mass-induction template defined in diquark quantum geometries.
The elementary 'God-Particle' is the heterotic superstring and not the Higgs Boson.
The diquark structure SUPPRESSES the mesonic Inner Ring (IR) in the magic diquark m=us and suppresses the dainty diquark D=dd in the leptonic OuterRing (OR) at the energy levels indicated and is bounded in the super quark of the S=ss at the energy levels indicated.
The so called charm quark forms a singlet as a Double-Up or U=uu as a up-quark family; the down quark family becomes a doublet in the bottom and the magic and the strange quark family forms a triplet as the dainty, the top and the super.
The Omicron resonance at the dainty level of 2x56 GeV or 112 GeV has for long been associated with the mass of the Higgs Boson, but is a simple suppressed diquark resonance at the doubledown quark eigenenergy.
Similarly, the 'pure' VPE annihilation of a W+ and a W- antimatter-matter weakon resonance of 160 GeV can be associated with the Higgs Boson mass as a OR-ORbar leptonic pair-annihilation eigenstate and as upper bound for a s.sbar coupling as a groundstate.
Of particular importance is however the 14 TeV energy realm of the LHC in the case the proton-proton collision were to become a 'pure' proton-antiproton collusion.
Because then no debris would eventuate in the discovery of the 'one and only''missing mass' particle of the RestMassPhoton as the hybrid of radiationmass, indicated in a previous message.
The superstringed Black Hole as the true 'God-Particle' is defined at an energy of 1,240 TeV in excess of the LHC energy by a factor of about 1000; but in terms of a spacetime metric, this energy as E* is calculated as 14.03 TeV via the formulation e*=Volume*.(df/dt)*=1/E* for a toroidal radius of R*=1.4x10-20 meters via V*=2π2R*3.
This represents the radius of the RMP as a hybrid boson coupling mass to radiation via the Planck-Einstein quantum formulation.
The LHC will indeed 'find' the 'God-Particle' at the proposed energy realm, but will not'see' it, due to 'too much' debris being 'in the way'.
sets the (PION-FAMILY: πo, π+, π-); the (STRANGE-Mean) specifies the (KAON-FAMILY: Ko, K+, K-); the (CHARM-Mean) defines the (J/PSI=J/Ψ-Charmonium-FAMILY); the (BEAUTY-Mean) sets the (UPSILON=Υ- Bottonium-FAMILY); the (MAGIC-Mean) specifies the (EPSILON=Ε-FAMILY); the (DAINTY-Mean) bases the (OMICRON-Ο-FAMILY); the (TRUTH-Mean) sets the (KOPPA=ς-Topomium-FAMILY) and the (SUPER-Mean) defines the final quark state in the (HIGGS/CHI=H/Χ-FAMILY).
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A new representation of the dispersion interaction

The conventional formulation of the dispersion energy as a power series in R −1 with damping at small R is re-examined. Symmetry-adapted and intermolecular perturbation theory calculations have been performed and compared for the argon dimer. We show that conventional Tang-Toennies damping functions fit the data better when exchange as well as charge-overlap effects are included. We also construct a new representation of the dispersion energy which provides a more accurate, but still quite compact, description of the dispersion energy, and suggest several simpler forms which would be suitable for describing dispersion more accurately in larger systems. Some preliminary results for the HF dimer are also described.<gh_stars>1-10
package core.utils

import java.time.LocalDateTime

import cats.data.Validated.{invalidNel, valid, Invalid, Valid}
import cats.data.{NonEmptyList, Validated, ValidatedNel}
import com.wix.accord
import com.wix.accord.RuleViolation
import com.wix.accord.combinators._
import core.failures.{Failure, GeneralFailure}

import scala.util.matching.Regex

trait Validation[M] {
  def validate: ValidatedNel[Failure, M]
}

object Validation {
  val prefix = "got"

  val ok: ValidatedNel[Failure, Unit] = valid(Unit)

  def isValid(predicate: Boolean, failure: ⇒ Failure): ValidatedNel[Failure, Unit] =
    if (predicate) valid(()) else invalidNel(failure)

  def validExpr(expression: Boolean, message: ⇒ String): ValidatedNel[Failure, Unit] =
    if (expression) valid({})
    else invalidNel(GeneralFailure(message))

  def isInvalid(predicate: Boolean, failure: