Search

Representing binary truth tables is an easy task to Boolean functions. When the number of Boolean variables increases, the complexity of the Boolean functions also increases. Thus, alternative ways of representing binary truth tables are necessary. It is known that this can be accomplished by means of other approaches, such as real polynomials. In the present paper it is shown that the recently introduced iota-delta function can be used to represent every binary truth table.

Conditional preference networks (CP-nets) are a compact but powerful formalism to represent and reason with qualitative preferences using the notion of conditional preferential independence. However, they suffer from incomparabilities between possible outcomes. Several works have attempted to overcome this weakness by quantifying CP-nets. This paper proposes a new approach combining two of the most interesting extensions of CP-nets, namely Probabilistic CP-nets (PCP-nets) using probability distribution to model uncertainty in different preference statements and Weighted CP-nets (WCP-nets) adding weights to express the relative importance of some attribute values regarding others. The new model so-called PWCP-nets combines the two models by handling both uncertainty and weights. Experimental results show the efficiency of this rich extension of CP-nets compared to PCP-nets and WCP-nets.

In this paper, we introduce arithmetic Heilbronn characters that generalize the notion of the classical Heilbronn characters, and discuss several properties of these characters. This formalism has several arithmetic applications. For instance, we obtain the holomorphy of suitable quotients of L-functions attached to elliptic curves, which is predicted by the Birch–Swinnerton–Dyer conjecture, and the non-existence of simple zeros or poles in such quotients.

In this paper, based on the thin-shell formalism, we introduce a classical model for particles in the framework of [Formula: see text]-dimensional [Formula: see text]-order pure Lovelock gravity. In particular, we construct a spherically symmetric particle of radius [Formula: see text] whose inside is a flat Minkowski spacetime while its outside is charged pLG solution. Knowing that in [Formula: see text]-dimensional spherically symmetric Einstein gravity ([Formula: see text]-gravity) such a particle model cannot be constructed, as we have discussed first, provides the main motivation for this study. In fact, it is the richness of Lovelock parameters that provides such a particle construction possible. On the thin-shell, the energy-momentum components are chosen to vanish, yet their normal derivatives are nonzero.

In this paper, we show that complete integrability is preserved in a multicomponent differential-difference Volterra system with branched dispersion relation. Using the Hirota bilinear formalism, we construct multisoliton solutions for a system of coupled [Formula: see text] equations. We also show that one can obtain the same solutions through a periodic reduction starting from a two-dimensional completely integrable generalized Volterra system. For some particular cases, graphical representations of solitons are displayed and stability is discussed using an asymptotic analysis.

This article has been retracted due to overlapping of its result with an earlier published article [Annals of Physics, Vol. 383 (2017) 497-510].

We investigate the relations between the black hole shadow and charged AdS black hole critical behaviour in the extended phase space. Using the thermo-shadow formalism built-in [1], we reveal that the shadow radius can be considered as an efficient tool to study thermodynamical black hole systems. Based on such arguments, we build a thermal profile by varying the RN-AdS black hole temperature on the shadow silhouette. Among others, the Van der Waals-like phase transition takes place. This could open a new window on the thermal picture of black holes and the corresponding thermodynamics from the observational point of view., Comment: 16 pages, 1 Tikz and 6 pdf figures, accepted in IJMPA

We discuss a new formalism for constructing a non-relativistic (NR) theory in curved background. Named as galilean gauge theory, it is based on gauging the global galilean symmetry. It provides a systematic algorithm for obtaining the covariant curved space time generalisation of any NR theory defined in flat space time. The resulting background is just the Newton- Cartan manifold. The example of NR free particle is explicitly demonstrated., 5 pages, Essay written for the Gravity Research Foundation 2020 Awards for Essays on Gravitation (Honorable mention) To appear in IJMPD (special issue)

In this paper, we have studied the transition and physical behavior of Bianchi type-V cosmological models within the formalism of [Formula: see text] gravity. To obtain the solution of field equations and phase transition of universe consistent with recent cosmological observations, time varying deceleration parameters are considered. In this paper, we used two different scale factors of the form (i) [Formula: see text], where [Formula: see text] are constants. Here, for [Formula: see text] the universe shows transition with accelerated expansion. (ii) [Formula: see text], where [Formula: see text] and [Formula: see text] are constants. For [Formula: see text], the universe achieves a phase transition from early decelerating to current accelerating phase. The model I initially starts with quintessence scenario ([Formula: see text]) and ends up with ([Formula: see text]) as a model with cosmological constant ([Formula: see text]) as [Formula: see text]. Model II, for [Formula: see text] indicates the phantom energy scenario and for [Formula: see text], the model starts with quintessence [Formula: see text] and ends with vacuum energy scenario. A point type singularity has been observed in the derived model I. Some physical and geometrical properties of the models have been established and discussed to derive the validity of models with respect to recent astrophysical observations.

The BRST quantization of the U(1) gauged model of FJ-type chiral boson for [Formula: see text] and [Formula: see text] are performed using the Batalin–Fradkin–Vilkovisky formalism. BFV formalism converts the second-class algebra into an effective first-class algebra with the help of auxiliary fields. Explicit expressions of the BRST charge, the involutive Hamiltonian, and the preserving BRST symmetry action are given and the full quantization has been carried through. For [Formula: see text], this Hamiltonian gives the gauge invariant Lagrangian including the well-known Wess–Zumino term, while for [Formula: see text] the corresponding Lagrangian has the additional new type of the Wess–Zumino term. The spectra in both cases have been analysed and the Wess–Zumino actions in terms of auxiliary fields are identified.

We study a stationary and axisymmetric binary system composed of two identical Kerr black holes, whose physical parameters satisfy the Smarr thermodynamic formula. Then, we use the formalism of geometrothermodynamics to show that the spatial distance between the black holes must be considered as a thermodynamic variable. We investigate the main thermodynamic properties of the system by using the contact structure of the phase space, which generates the first law of thermodynamics and the equilibrium conditions. The phase transition structure of the system is investigated through the curvature singularities of the equilibrium space. It is shown that the thermodynamic and stability properties and the phase transition structure of the binary system strongly depend on the distance between the black holes., Comments and references added

We study a braneworld Randall–Sundrum type II (RSII) model using the Hamilton–Jacobi formalism. We extend the standard inflationary parameters and the flow equations for this braneworld scenario. We investigate the conditions that reduce the infinite number of flow equations into a finite number and confirm that by considering one of the inflationary parameters that vanishes, the Hubble expansion rate gets a polynomial form in both General Relativity (GR) and in the high-energy regime of RSII. We also show that if one sets this inflationary parameter to a constant value, the model features a nonpolynomial form of the Hubble expansion rate. The form of the Hubble parameter in this case is different in GR and RSII. Next, we consider a single-scalar field model with a Hubble expansion rate behaving as [Formula: see text] and show that compared to GR, the RSII model has a smaller tensor-to-scalar ratio and larger spectral index for [Formula: see text]. Therefore, RSII model leads to better predictions than GR.

A brief review of our previously introduced forward and backward in time formalism for non-relativistic electron diffraction and its relativistic extension to study photons in time and space is presented. The zero-point energy in the Planck black body spectrum emerges naturally once time-symmetric motion — inherent in Maxwell equations — is invoked for photons. A study of two-slit experiments for slits smaller than the wavelength of the photon unravels novel phenomena due to the spin of the photon. Our proposed experiments are within reach of present technology and could be of interest for modern imaging and quantum optics.

In this work we consider the scale-covariant formalism proposed by Canuto et al.,[Formula: see text] in order to map different eras of the universe. This technique considers a scale gauge function that can be adjusted by using different arguments like Dirac’s large numbers hypothesis or a restriction on the particle production rate. A Chaplygin constituent shows to be a consistent idea to establish a mapping between an old decelerated–accelerated universe ruled by Einstein equations and an early universe, where a new equation of state appears together with a modified general relativity theory and a de Sitter universe then emerges. These properties are a direct consequence of the use of the scale-covariant formalism. Besides, a new discussion and remarks are presented related to the well-known barotropic constituent case.

This note gives an overview on basic mathematical models describing the population dynamics of a single species whose vital dynamics has different time scales. We present five cases combining two time–scales with Malthusian growth in at least one scale. The dynamical behavior shows a progressive complexity, from "naive" to chaotic dynamics (in the Li–Yorke's sense). In addition, some open problems and new results are presented.

In this paper, we studied the dynamics of thin shell in the perfect fluid composed of scalar field. To formulate the equation of motion of the shell, we used the Israel thin-shell formalism for the Brane-world black hole in the two surrounding vacuum regions (interior and exterior). In this study, we considered the potential function as a quadratic function of scalar field. The resulting dynamical equations have been analyzed numerically for both the cases, massless and massive scalar field through the effective potential and radius of the shell by considering different settings of the parameters involved. We found that there are three possibilities in this geometry, thin shell in the scalar field can expand, collapse or attain equilibrium for a while, however, in most of the cases for large value of radius, thin shell collapses to zero size. The effects of the parameters [Formula: see text] and [Formula: see text] (involved due to the Brane-world geometry) on the expansion and collapsing rates have been analyzed and the obtained results compared with the Schwarzschild case ([Formula: see text], [Formula: see text]).

This paper is devoted to the study of the stability of thin-shell wormholes from Kerr black hole. We employ Israel thin-shell formalism to evaluate surface stresses and study the behavior of energy conditions. The linearized stability of rotating thin-shell wormholes is analyzed by taking two different candidates of dark energy as exotic matter at thin-shell. It is found that generalized phantom model ([Formula: see text] which reduces to phantom equation of state as [Formula: see text] and [Formula: see text], where [Formula: see text] is wormhole throat radius and [Formula: see text] is the proper time) yields more stable wormhole solutions as compared to the barotropic equation of state ([Formula: see text], [Formula: see text] is the equation of state parameter and [Formula: see text] is the surface density) for particular ranges of equilibrium throat radius and the whole range of [Formula: see text].

Propagator for spinning particle described in the Feshbach–Villars formalism is set up using the bosonic coherent state path integral. The boson model for the charge-spin symmetry is presented following the Schwinger recipe. The calculations are explicitly evaluated in the case of the step potential. The perturbation technique is used and the series are exactly summed.

In the present paper, we develop a picture formalism which gives rise to an invariant that dominates several known invariants of classical and virtual knots: the Jones polynomial [Formula: see text], the Kuperberg bracket [Formula: see text], and the normalized arrow polynomial [Formula: see text].

We address the problem of distributed quantum metrology with a single squeezed-vacuum source by using the formalism of quantum mechanics in phase space. In particular, we demonstrate Heisenberg-limited sensitivity in the measurement of the average of two arbitrary phase shifts in the arms of a Mach–Zehnder interferometer. We obtain exact results for the measurement probability at the interferometer output for any value of the phases, which give us insight into the emergence of Heisenberg-limited sensitivity for periodical values of the phases.

We extend Howland time-independent formalism to the case of completely positive and trace preserving dynamics of finite dimensional open quantum systems governed by periodic, time dependent Lindbladian in Weak Coupling Limit, expanding our result from previous papers. We propose the Bochner space of periodic, square integrable matrix valued functions, as well as its tensor product representation, as the generalized space of states within the time-independent formalism. We examine some densely defined operators on this space, together with their Fourier-like expansions and address some problems related to their convergence by employing general results on Banach-space valued Fourier series, such as the generalized Carleson-Hunt theorem. We formulate Markovian dynamics in the generalized space of states by constructing appropriate time-independent Lindbladian in standard (Lindblad-Gorini-Kossakowski-Sudarshan) form, as well as one-parameter semigroup of bounded evolution maps. We show their similarity with Markovian generators and dynamical maps defined on matrix space, i.e. the generator still possesses a standard form (extended by closed perturbation) and the resulting semigroup is also completely positive, trace preserving and a contraction., 33 pages, no figures; revised version

In our previous paper I (del Valle--Turbiner, Int. J. Mod. Phys. A34, 1950143, 2019) it was developed the formalism to study the general $D$-dimensional radial anharmonic oscillator with potential $V(r)= \frac{1}{g^2}\,\hat{V}(gr)$. It was based on the Perturbation Theory (PT) in powers of $g$ (weak coupling regime) and in inverse, fractional powers of $g$ (strong coupling regime) in both $r$-space and in $(gr)$-space, respectively. As the result it was introduced - the Approximant - a locally-accurate uniform compact approximation of a wave function. If taken as a trial function in variational calculations it has led to variational energies of unprecedented accuracy for cubic anharmonic oscillator. In this paper the formalism is applied to both quartic and sextic, spherically-symmetric radial anharmonic oscillators with two term potentials $V(r)= r^2 + g^{2(m-1)}\, r^{2m}, m=2,3$, respectively. It is shown that a two-parametric Approximant for quartic oscillator and a five-parametric one for sextic oscillator for the first four eigenstates used to calculate the variational energy are accurate in 8-12 figures for any $D=1,2,3\ldots $ and $g \geq 0$, while the relative deviation of the Approximant from the exact eigenfunction is less than $10^{-6}$ for any $r \geq 0$., 52 pages, 17 figures, 3 appendices

The standard regular expressions over finite alphabets have been widely accepted as the most basic formalism to query graph databases. However, the major drawback of this approach is that it ignores the presence of data. In this paper we study the so called {\em regular expressions with binding} (REWB), that is, regular expressions equipped with variables to store data within a well defined scope. In particular, we study the complexity of the query evaluation of REWB queries over graph databases. FWO Pegasus Marie Curie Fellowship

This paper presents a guideline to systematically design and construct a micro quadrotor unmanned aerial vehicle (UAV), capable of autonomous flight. The designed micro UAV has a gross weight of less than 40 g including power supply sufficient for an 8-min flight. The design is divided into three parts. First, investigation is made on the structural design of a conventional quadrotor. The quadrotor frame is then carefully designed to avoid any potential structural natural frequencies within the range of rotors operating speeds, based on simulation results obtained from MSC Nastran. Second, avionic system of the aircraft will be discussed in detail, mainly focusing on the design of printed circuit boards which include sensors, microprocessors and four electronic speed controllers, specially catered for micro quadrotor design. Last, a mathematical model for the micro quadrotor is derived based on Newton–Euler formalism, followed by methods of identifying the parameters. The flight test results are later described, analyzed and illustrated in this paper.

The phase structure of charged Anti-de Sitter black hole in massive gravity is investigated using the unstable circular photon orbits formalism, concretely we establish a direct link between the null geodesics and the critical behavior thermodynamic of such black hole solution. Our analysis reveals that the radius and the impact parameter corresponding to the unstable circular orbits can be used to probe the thermodynamic phase structure. We also show that the latter are key quantities to characterize the order of Van der Waals-like phase transition. Namely, we found a critical exponent around $ \delta = 1/2 $. All these results support further that the photon trajectories can be used as a useful and crucial tool to probe the thermodynamic black holes criticality., Comment: 15 pages, 5 figures, two paragraphs modified, added references

Three-dimensional structures of 62 polychlorinated biphenyl (PCB) congeners were optimized with the integral equation formalism polarizable continuum model (IEF-PCM) in combination with the density functional theory (DFT) method at 6-31G(d) level. By applying support vector machine (SVM) algorithm, a nonlinear quantitative structure–property relationship (QSPR) model was built to predict half-lives (log [Formula: see text]) of 62 PCBs in juvenile rainbow trout. The optimal SVM model based on the parameters [Formula: see text] of 854.721 and [Formula: see text] of 0.0565 produces the root-mean-square (rms) errors of 0.0352 for the training set and 0.0446 for the test set, which are less than that of the previous models reported. The results suggest that it is feasible to build SVM models for the half-lives of PCBs with IEF-PCM and B3LYP/6-31G(d) for deriving structural descriptors.

The mechanical, electronic and thermodynamic properties of Pd3M (M[Formula: see text]=[Formula: see text]Sc, Y) compounds have been investigated using the Full Potential Linearized Augmented Plane Wave (FP-LAPW) formalism. The generalized gradient approximation (GGA) is used to treat the exchange–correlation terms. The calculated formation enthalpies and the cohesive energies reveal that the L12 structure is more stable than the D0[Formula: see text] one. The obtained lattice parameters and bulk modulus calculations conform well to the available experimental and theoretical results. The elastic and mechanical properties are analyzed and results show that both compounds are ductile in nature. The Debye temperature and melting temperature are also estimated and are in a good agreement with experimental findings. The total and partial densities of states are determined for L12 and D0[Formula: see text] structures. The density of states at the Fermi level, [Formula: see text]([Formula: see text]), indicates electronic stability for both compounds. The presence of the pseudo-gap near the Fermi level is suggestive of formation of directional covalent bonding. The number of bonding electrons per atom [Formula: see text] and the electronic specific heat coefficient [Formula: see text] are also determined. The quasi-harmonic Debye model has been used to explore the temperature and pressure effects on the thermodynamic properties for both compounds.

We discuss the quantum theory of an harmonic oscillator with time-dependent mass and frequency submitted to action of a complex time-dependent linear potential with [Formula: see text] symmetry. Combining the Lewis and Riesenfeld approach to time-dependent non-Hermitian Hamiltonians having [Formula: see text] symmetry and linear invariants, we solve the time-dependent Schrödinger equation for this problem and use the corresponding quantum states to construct a Gaussian wave packet solution. We show that the shape of this wave packet does not depend on the driving force. Afterwards, using this wave packet state, we calculate the expectation values of the position and momentum, their fluctuations and the associated uncertainty product. We find that these expectation values are complex numbers and as a consequence the position and momentum operators are not physical observables and the uncertainty product is physically unacceptable.

A model for an anisotropic pre-inflationary universe described by the Bianchi type-I metric is developed. A relativistic fluid of the Schutz formalism and a self-interacting fermionic field are considered as sources of the gravitational field. The classical analysis is based on the Hamiltonian formalism written in terms of the Misner variables and it is shown that the fluid degrees of freedom can be embodied by a conformal time variable. The three classical scale factors are obtained as functions of the conformal time. The quantum analysis follows from the de Broglie–Bohm formalism applied to the wave function which is a solution of the Wheeler–DeWitt equation and the three scale factors are also determined as functions of the conformal time. While the classical expressions for the scale factors show a singularity when the conformal time vanishes, their quantum expressions exhibit bouncing behavior. It is possible to adjust the behavior of the classical and quantum scale factors as functions of the conformal time so that they have a common isotropic behavior at late times with a dilution of the quantum effects.

In this work, we show the importance of introducing the quantum tomography formalism to analyze the properties of wave functions in quantum cosmology. In particular, we examine the initial conditions of the universe proposed by various authors in the context of de Sitter’s cosmology studying their classical limit and comparing it with the classical tomogram obtained from the Hamiltonian constraint in General Relativity. This comparison gives us the opportunity to find under which conditions there is a transition from the quantum universe to the classical one. A relevant result is that in these models the decay of the cosmological constant is a sufficient condition for this transition.

In this contribution, we provide a theoretical model to study the effect of different cutting edges on the appearance of localized electronic states. The system under study is a three-dimensional atomic chain that ends with an open cut forming a semi-infinite structured layer in the (1 0 0), (1 1 0) and (1 1 1) directions. We investigate the surface electronic characteristics of the monoatomic chain of a simple cube (sc), orthorhombic (orth), and tetragonal (tetr) structures. We have adopted in our approach the tight-binding approximation to build up the surface Hamiltonian matrix. Additionally, the number of secular equation, at the surface, has been determined by using phase field matching theory (FPMT). In fact, the Hamiltonian system obtained from different cutting orientations provides an inhomogeneous system. To solve the surface eigenvalue problem, we integrate the calculation of the scattering reflection probabilities as given in Landauer–Büttiker formalism. Next, based on the computed scattering probabilities, we build up the surface core states which provide the surface Hamiltonian matrix which can be solved numerically. Our model calculation has been applied to the following elements: (i) fluorite (F), manganese (Mn), polonium (Po), bromine (Br), indium (I), tin (Sn), and protactinium (Pa). The results emphasize the influence of cutting direction on the electronic characteristic of surface and on the scale of energy values. We report the appearance of new electronic curves that characterize the surface states. Those surface states are localized down, within, and above the bulk spectrum. They also provide different characteristic features, of the metals under study, in a given cutting orientation. Furthermore, we have integrated the calculation of non-structured cuts on the outer layers. The relaxation effect on the surface is a standard process which leads to stabilize the changes in the internal energy until the equilibrium. The spacing geometry caused by the relaxation on the surface could be determined by using the molecular dynamic algorithm. We account in this case the lift of degeneracy and the rise of additional localized branches within and outside the bulk range.

This paper studies the dynamics of thin-shell for (2 + 1)-dimensional rotating and charged rotating Bañados–Teitelboim–Zanelli black holes by using Israel thin-shell formalism. We consider the matter distribution located at thin-shell associated with a scalar field and analyze its effects on the dynamics of thin-shell through equations of motion and effective potential. The corresponding dynamical equations are numerically studied for both massless as well as massive scalar fields. For rotating case, the rate of expansion and collapse increases with massless scalar shell but decreases for massive case. For charged rotating, the rate of expansion and collapse decreases by increasing angular momentum for both massless as well as massive case. We conclude that the rate of expansion and collapse of the rotating case is greater than charged rotating black hole.

The aim of this paper is to study the gravitational collapse of charged cylindrical star in [Formula: see text] gravity. For this purpose, we derive dynamical equations by applying Misner–Sharp formalism and examine the effects of effective pressure and charge on the collapse rate. We also construct a relationship between matter variables, Gauss–Bonnet (GB) terms, and the Weyl tensor. For the constant value of [Formula: see text], it is found that spacetime is conformally flat if and only if the energy density is homogeneous. We conclude that the rate of collapse slows down in [Formula: see text] gravity due to anti-gravitational effects.

In the context of Clifford functional integral formalism, we revisit the Nambu-Jona-Lasinio-type dynamical symmetry breaking model and examine the properties of the dynamically generated composite bosons. Given that the model with 4-fermion interactions is nonrenormalizable in the traditional sense, the aim is to gain insight into the divergent integrals without resorting to explicit regularization. We impose a restriction on the linearly divergent primitive integrals, thus resolving the long-standing issue of momentum routing ambiguity associated with fermion-antifermion condensations. The removal of the ambiguity paves the way for the possible calculation of the true ratio of Higgs boson mass to top quark mass in the top condensation model. In this paper, we also investigate the negative vacuum energy resulted from dynamical symmetry breaking and its cosmological implications. In the framework of modified Einstein-Cartan gravity, it is demonstrated that the late-time acceleration is driven by a novel way of embedding the Hubble parameter into the Friedmann equation via an interpolation function, whereas the dynamically generated negative cosmological constant only plays a minor role for the current epoch. Two cosmic scenarios are proposed, with one of which suggesting that the universe may have been evolving from an everlasting coasting state towards the accelerating era characterized by the deceleration parameter approaching -0.5 at low redshift. One inevitable outcome of the modified Friedmannian cosmology is that the directly measured local Hubble parameter should in general be larger than the Hubble parameter calibrated from the conventional Friedmann equation. This Hubble tension becomes more pronounced when the Hubble parameter is comparable or less than a characteristic Hubble scale., 30 pages

We derive the entangled thermal mixed states by using the formalism of phase states for a finite-dimensional algebra of a multi-qubit system in contact with an independent thermal environment of absolute temperature [Formula: see text]. Thermal entangled states describing the multi-qubit system in equilibrium with the thermal bath are a special kind of mixed states that exhibit genuine multipartite correlation. We define the unitary phase operators for a multipartite system of non-interacting qubits. Entangled density matrices are derived for qubits interacting via an Hermitian Hamiltonian of Heisenberg type [Formula: see text]. By assuming that the noisy interaction of the entangled qubit ensemble with the bath is governed by a local Hamiltonian [Formula: see text], we show that the entangled phase states can be decohered. When the multi-qubits entangled system reaches the equilibrium with the thermal bath, the decohered mixed states are identified with entangled thermal states. The thermal mixed states for bipartite and multipartite systems are explicitly expressed and their bipartite entanglement properties are investigated.

This paper deals with warm viscous inflation inspired by tachyon field using an important inflationary method known as Hamilton–Jacobi’s Formalism. This method provides a way to solve the equations of inflationary model without using extra approximations other than slow-roll. In this scenario, a general inflationary formalism is developed for tachyon field and the work is restricted to high dissipative regime. A detailed analysis of the model is presented for three different cases of constant as well as variable bulk and dissipative coefficients. In each case, the model parameters are constrained to plot the physically acceptable range of the perturbed parameters. The parametric trajectories proved that the acquired results for all cases are compatible with Planck astrophysical data.

Propagator for spinning particle described in the Feshbach–Villars formalism is set up using fermionic coherent state path integral. The fermionization of the charge-spin symmetry is presented following the Schwinger recipe. The explicit calculations are done in the free case and magnetic interaction using the Foldy–Wouthuysen tranformation. The spectrum and wave functions are deduced.

We consider the holomorphic twist of the worldvolume theory of flat D$(2k-1)$-branes transversely probing a Calabi--Yau manifold. A chain complex, constructed using the BV formalism, computes the local observables in the holomorphically twisted theory. Generalizing earlier work in the case $k=2$, we find that this complex can be identified with the Ginzburg dg algebra associated to the Calabi--Yau. However, the identification is subtle; the complex is the space of fields contributing to the holomorphic twist of the free theory, and its differential arises from interactions. For $k=1$, this holomorphically twisted theory is related to the elliptic genus. We give a general description for D1-branes probing a Calabi--Yau fourfold singularity, and for $\mathcal{N}=(0,2)$ quiver gauge theories. In addition, we propose a relation between the equivariant Hirzebruch $\chi_y$ genus of large-$N$ symmetric products and cyclic homology., Comment: 55 pages, 6 figures, 8 tables

Starting from the classical nonrelativistic electrodynamics in 1[Formula: see text]+[Formula: see text]1 dimensions, a higher-derivative version is proposed. This is made by adding a suitable higher-derivative term for the electromagnetic field to the Lagrangian of the original electrodynamics, preserving its gauge invariance. By following the usual Hamiltonian method for singular higher-derivative systems, the canonical quantization for the higher-derivative model is developed. By extending the Faddeev–Senjanovic algorithm, the path integral quantization is carried out. Hence, the Feynman rules are established and the diagrammatic structure is analyzed. The use of the higher-derivative term eliminates in the Landau gauge the ultraviolet divergence of the primitively divergent Feynman diagrams of the original model, where the electromagnetic field propagator is present. A generalization of the BRST quantization is also considered.

This article provides a review of control protocol synthesis techniques that incorporate methodologies from formal methods and control theory to provide correctness guarantee for different types of autonomous systems, including those with discrete and continuous state space. The correctness of the system is defined with respect to a given specification expressed as a formula in linear temporal logic to precisely describe the desired properties of the system. The formalism presented in this article admits nondeterminism, allowing uncertainties in the system to be captured. A particular emphasis is on alleviating some of the difficulties, e.g., heterogeneity in the underlying dynamics and computational complexity, that naturally arise in the construction of control protocols for autonomous systems.

Recent results in Local Regge Calculus are confronted with Spin Foam Formalism. Introducing Barrett-Crane Quantization in Local Regge Calculus makes it possible to associate a unique Spin jh with an hinge h, fulfilling one of the requirements of Spin Foam definition. It is shown that inter-twiner terms of Spin Foam can follow from the closure constraint in Local Regge Calculus.

By applying nonequilibrium Green's function formalism combined with first-principles density functional theory, we investigate the effect of torsion angle on the rectifying performance in the donor-bridge-acceptor single molecular device. The influence of HOMO–LUMO gaps and the spatial distributions of molecular orbitals on the electronic transport through the molecular device are discussed in detail. The theoretical results show that the torsion angle plays an important role in the rectifying behavior of such devices. By changing the torsion angle, namely changing the magnitude of the intermolecular coupling effect, a different rectifying behavior can be observed in these systems. The results can provide fundamental guidelines for the design of functional molecular devices to a certain extent.

We study the evolution of degree distributions of susceptible-infected-susceptible (SIS) model on random networks, where susceptible nodes are capable of being infected, and infected nodes can spread the disease further. The network of contacts is modeled as a configuration model featuring heterogeneous degree distribution. We derive systematically the (excess) degree distributions among susceptible and infected individuals by using the probability generating function formalism.

Ever since Werner Heisenberg's 1927 paper on uncertainty, there has been considerable hesitancy in simultaneously considering positions and momenta in quantum contexts, since these are incompatible observables. But this persistent discomfort with addressing positions and momenta jointly in the quantum world is not really warranted, as was first fully appreciated by Hilbrand Groenewold and Jos\'e Moyal in the 1940s. While the formalism for quantum mechanics in phase space was wholly cast at that time, it was not completely understood nor widely known --- much less generally accepted --- until the late 20th century., Comment: A brief history of deformation quantization, ca 1930-1960, with some elementary illustrations of the theory

The Fock-Tani representation, is a field theoretic formalism to treat problems involving both composite particles and their constituents. The application of the Fock-Tani transformation to a pair creation Hamiltonian produces the characteristic expansion in powers of the wave function. In lowest order of this expansion, we obtain the model known in the literature: the 3P0 model. In higher orders, the Corrected 3P0 model (C3P0) is obtained by introducing the bound state kernel. In this work, we use the C3P0 model to calculate the J/ψ decay rates in the following channels: ρ π, ω η, ω η′, K*+ K-, [Formula: see text], ϕ η, ϕ η′. We consider that the J/ψ is a mixture given by [Formula: see text].

The Fock-Tani formalism is a successful mapping technique that has been used in hadron physics to describe hadron interaction and decay. In this one can obtain the 3P0 model with bound state corrections. In this work we applay this technique for [Formula: see text] decay, where the amplitude and its respective decay rates are evaluated.

We use a self-consistent chiral-hydrodynamic formalism which combines the linear $\sigma$ model with second-order hydrodynamics in 2+1 dimensions to compute the spectrum of thermal photons produced in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV. The temperature-dependent shear viscosity of the model, $\eta$, is calculated from the linearized Boltzmann equation. We compare the results obtained in the chiral-hydrodynamic model to those obtained in the second-order theory with a Lattice QCD equation of state and a temperature-independent value of $\eta/s$. We find that the thermal photon production is significantly larger in the latter model due to a slower evolution and larger dissipative effects., Comment: 5 pages, 2 figures. To appear in Int. J. Mod. Phys.: Conference Series, Proceedings of IWARA 2011

The purpose of this paper is to test the validity of the thin shell formalism. Firstly, we construct a dust thick shell collapsing to a Schwarzschild black hole. From this exact solution, we show that the two sides of the shell satisfy different equations of motion. Moreover, we show that the inner side and the outer side always cross each other right after the formation of the thin shell, causing a breakdown of the model. Secondly, we establish a class of wormholes with non-zero thickness and extremal Reissner-Nordström exterior. In the thin shell limit, we find that the surface stress-energy tensor contains the contribution of electromagnetic field, which contradicts the assumption in previous literature.

In this work we have discussed dependence of surface tension coefficient that appears in proximity potential and energy of incident nucleus. The obtained results from study of the fusion barrier heights and positions for 44 reactions with z≥8 reveal that this modification on the formalism of proximity model leads to a better agreement between computed fusion barrier heights and positions and experimental data.

The relativistic four-quark equations are found in the framework of coupled-channel formalism. The dynamical mixing of the meson-meson states with the four-quark states is considered. The four-quark amplitudes of the negative parity tetraquarks including the quarks of three flavors (u, d, s) and the charmed quark are constructed. The poles of these amplitudes determine the masses of tetraquarks. The mass values of low-lying tetraquarks with the spin-parity JP=0-,1-,2-,3- are calculated., 18 pages, pdf