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An H-matrix accelerated direct solver employing the high-order Chebyshev-based Boundary Integral Equation (CBIE) method has been formulated, tested, and profiled for performance on high contrast dielectric materials and electrically large perfect electric conductor objects. The matrix fill performance of the CBIE proves to be fast for small to moderately sized problems compared to its counterparts, e.g. the locally corrected Nystr\"om (LCN) method, due to the way it handles the singularities by means of a global change of variable method. However, in the case of electrically large scattering problems, the matrix fill and factorization still dominate the solution time when using a direct solution approach. To address this issue, an H-Matrix framework is employed, effectively resolving the challenge and establishing the CBIE as a competitive high-order method for solving scattering problems with poorly conditioned matrix equations. The efficacy of this approach is demonstrated through extensive numerical results, showcasing its robustness to problems that are electrically large, near physical resonances, or that have large dielectric permittivities. The capability of the proposed solver for handling arbitrary geometries is also demonstrated by considering various scattering examples from complex CAD models.

The existing paradox between theory and computational experiment for weak solutions of systems of conservation laws in higher space dimensions is arguably resolved. Apparently successful computations are identified with underlying boundary-value problems which are well-posed only in a weakened sense. In the absence of hyperbolicity in particular, prescribed boundary data sufficient to determine an a priori bound for an entropy weak solution need not suffice to imply local uniqueness thereof. In this context, fluid flow models based on stationary or self-similar reductions of Euler systems are distinguished as particularly attractive for computational investigation.

Humanitarian action is accompanied by a mass of reports, summaries, news, and other documents. To guide its activities, important information must be quickly extracted from such free-text resources. Quantities, such as the number of people affected, amount of aid distributed, or the extent of infrastructure damage, are central to emergency response and anticipatory action. In this work, we contribute an annotated dataset for the humanitarian domain for the extraction of such quantitative information, along side its important context, including units it refers to, any modifiers, and the relevant event. Further, we develop a custom Natural Language Processing pipeline to extract the quantities alongside their units, and evaluate it in comparison to baseline and recent literature. The proposed model achieves a consistent improvement in the performance, especially in the documents pertaining to the Dominican Republic and select African countries. We make the dataset and code available to the research community to continue the improvement of NLP tools for the humanitarian domain.

Radium-225 (nuclear spin $I=1/2$) ions possess electronic hyperfine transitions that are first-order insensitive to magnetic field noise, which is advantageous for optical clocks and quantum information science. We report on laser cooling and trapping of radium-225 ions and hyperfine splitting measurements of the ion's $7s$ $^2S_{1/2}$, $7p$ $^2P_{1/2}$, and $6d$ $^2D_{3/2}$ states. We measured the ground state hyperfine constant, $A(^2S_{1/2}) = -27.684511056(9)\ \mathrm{GHz}$, and the quadratic Zeeman coefficient, $C_2 = 142.3(10)\ \mathrm{Hz\ G}^{-2}$, of the $^2S_{1/2} (F=0, m_F = 0) \leftrightarrow~^2S_{1/2} (F=1, m_{F} = 0)$ transition. We also measured the hyperfine constants of the $^2P_{1/2}$ state, $A(^2P_{1/2}) = -5.447(4)\ \mathrm{GHz}$, and the $^2D_{3/2}$ state, $A(^2D_{3/2}) = -619.7(11)\ \mathrm{MHz}$., Comment: 5 pages, 4 figures

We study a class of renormalization group flows on line defects that can be described by a generalized free field with ordered planar contractions on the line. They are realized, for example, in large $N$ gauge theories with matter in the fundamental representation and arise generically in non-relativistic CFTs. We analyze the flow exactly and compute the change in the $g$-function between the UV and IR fixed points. We relate the result to the change in the two-point function of the displacement operator and check the monotonicity of the defect entropy along the flow analytically. Finally, we give a general realization of this type of flow starting from the direct sum of the IR fixed point and a trivial line. This type of defect renormalization group flow parallels the well-studied case of double-trace flow., Comment: 21 pages, 4 figures; v2: improved presentation; v3: improved presentation and fixed typos

The expectation value of a smooth conformal line defect in a CFT is a conformal invariant functional of its path in space-time. For example, in large $N$ holographic theories, these fundamental observables are dual to the open string partition function in AdS. In this paper, we develop a bootstrap method for studying them and apply it to conformal line defects in Chern-Simons matter theories. In these cases, the line bootstrap is based on three minimal assumptions -- conformal invariance of the line defect, large $N$ factorization, and the spectrum of the two lowest-lying operators at the end of the line. On the basis of these assumptions, we solve the one-dimensional CFT on the line and systematically compute the defect expectation value in an expansion around the straight line. We find that the conformal symmetry of a straight defect is insufficient to fix the answer. Instead, imposing the conformal symmetry of the defect along an arbitrary curved line leads to a functional bootstrap constraint. The solution to this constraint is found to be unique., Comment: 33 pages. v2: Typos corrected. JHEP version

A critical task for developing safe autonomous driving stacks is to determine whether an obstacle is safety-critical, i.e., poses an imminent threat to the autonomous vehicle. Our previous work showed that Hamilton Jacobi reachability theory can be applied to compute interaction-dynamics-aware perception safety zones that better inform an ego vehicle's perception module which obstacles are considered safety-critical. For completeness, these zones are typically larger than absolutely necessary, forcing the perception module to pay attention to a larger collection of objects for the sake of conservatism. As an improvement, we propose a maneuver-based decomposition of our safety zones that leverages information about the ego maneuver to reduce the zone volume. In particular, we propose a "temporal convolution" operation that produces safety zones for specific ego maneuvers, thus limiting the ego's behavior to reduce the size of the safety zones. We show with numerical experiments that maneuver-based zones are significantly smaller (up to 76% size reduction) than the baseline while maintaining completeness., Comment: * indicates equal contribution. Accepted into the IEEE Intelligent Vehicles Symposium 2023

The famous result of Lindemann and Weierstrass says that if $a_{1},a_{2},\ldots,a_{n}$ are distinct algebraic numbers, then $e^{a_{1}},e^{a_{2}},\ldots,e^{a_{n}}$ are linearly independent complex numbers over the field $\overline{\mathbb{Q}}$ of all algebraic numbers. Starting from some basic ideas of Hermite, Lindemann, Hilbert, Hurwitz and Baker, in this note we provide an easy to understand and self-contained proof for the Lindemann-Weierstrass Theorem. In an introductory section we have gathered all the algebraic number theory tools that are necessary to prove the main theorem. All these auxiliary results are fully proved in a simple and elementary way, so that the paper can be read even by an undergraduate student., Comment: 17 pages, minor corrections and latex updates

We report bound state solutions of the Klein Gordon equation with a novel combined potential, the Eckart plus a class of Yukawa potential, by means of the parametric Nikiforov-Uvarov method. To deal the centrifugal and the coulombic behavior terms, we apply the Greene-Aldrich approximation scheme. We present any $\ell$-state energy eigenvalues and the corresponding normalized wave functions of a mentioned system in a closed form. We discuss various special cases related to our considered potential which are utility for other physical systems and show that these are consistent with previous reports in literature. Moreover, we calculate the non-relativistic thermodynamic quantities (partition function, mean energy, free energy, specific heat and entropy) for the potential model in question, and investigate them for a few diatomic molecules. We find that the energy eigenvalues are sensitive with regard to the quantum numbers $n_r$ and $\ell$ as well as the parameter $\delta$. Our results show that energy eigenvalues are more bounded at either smaller quantum number $\ell$ or smaller parameter $\delta$., Comment: 18 pages, 33 figures, 2 tables. Thermodynamic predictions for several diatomic molecules have been added in the new version

We argue that for any single-trace operator in ${\cal N}=4$ SYM theory there is a large twist double-scaling limit in which the Feynman graphs have an iterative structure. Such structure can be recast using a graph-building operator. Generically, this operator mixes between single-trace operators with different scaling limits. The mixing captures both the finite coupling spectrum and corrections away from the large twist limit. We first consider a class of short operators with gluons and fermions for which such mixing problems do not arise, and derive their finite coupling spectra. We then focus on a class of long operators with gluons that do mix. We invert their graph-building operator and prove its integrability. The picture that emerges from this work opens the door to a systematic expansion of ${\cal N}=4$ SYM theory around the large twist limit., Comment: 54 pages, 16 figures

The rising use of microservices based software deployment on the cloud leverages containerized software extensively. The security of applications running inside containers as well as the container environment itself are critical infrastructure in the cloud setting and 5G. To address the security concerns, research efforts have been focused on container security with subfields such as intrusion detection, malware detection and container placement strategies. These security efforts are roughly divided into two categories: rule based approaches and machine learning that can respond to novel threats. In this study, we have surveyed the container security literature focusing on approaches that leverage machine learning to address security challenges., Comment: 14 pages, 2 tables, 1 figure, submitted to Special issue on AI-driven security in 5G and beyond

Development of guidance, navigation and control frameworks/algorithms for swarms attracted significant attention in recent years. That being said, algorithms for planning swarm allocations/trajectories for engaging with enemy swarms is largely an understudied problem. Although small-scale scenarios can be addressed with tools from differential game theory, existing approaches fail to scale for large-scale multi-agent pursuit evasion (PE) scenarios. In this work, we propose a reinforcement learning (RL) based framework to decompose to large-scale swarm engagement problems into a number of independent multi-agent pursuit-evasion games. We simulate a variety of multi-agent PE scenarios, where finite time capture is guaranteed under certain conditions. The calculated PE statistics are provided as a reward signal to the high level allocation layer, which uses an RL algorithm to allocate controlled swarm units to eliminate enemy swarm units with maximum efficiency. We verify our approach in large-scale swarm-to-swarm engagement simulations., Comment: Accepted to SciTech2023

We study mesonic line operators in Chern-Simons theories with bosonic or fermionic matter in the fundamental representation. In this paper, we elaborate on the classification and properties of these operators using all loop resummation of large $N$ perturbation theory. We show that these theories possess two conformal line operators in the fundamental representation. One is a stable renormalization group fixed point, while the other is unstable. They satisfy first-order chiral evolution equations, in which a smooth variation of the path is given by a factorized product of two mesonic line operators. The boundary operators on which the lines can end are classified by their conformal dimension and transverse spin, which we compute explicitly at finite 't Hooft coupling. We match the operators in the bosonic and fermionic theories., Comment: 105 pages, 17 figures. v2: extended to mass deformed CS-matter theories, (section 8). Some details about anomalous spin moved to appendix. Typos corrected. JHEP version

To enable safe autonomous vehicle (AV) operations, it is critical that an AV's obstacle detection module can reliably detect obstacles that pose a safety threat (i.e., are safety-critical). It is therefore desirable that the evaluation metric for the perception system captures the safety-criticality of objects. Unfortunately, existing perception evaluation metrics tend to make strong assumptions about the objects and ignore the dynamic interactions between agents, and thus do not accurately capture the safety risks in reality. To address these shortcomings, we introduce an interaction-dynamics-aware obstacle detection evaluation metric by accounting for closed-loop dynamic interactions between an ego vehicle and obstacles in the scene. By borrowing existing theory from optimal control theory, namely Hamilton-Jacobi reachability, we present a computationally tractable method for constructing a ``safety zone'': a region in state space that defines where safety-critical obstacles lie for the purpose of defining safety metrics. Our proposed safety zone is mathematically complete, and can be easily computed to reflect a variety of safety requirements. Using an off-the-shelf detection algorithm from the nuScenes detection challenge leaderboard, we demonstrate that our approach is computationally lightweight, and can better capture safety-critical perception errors than a baseline approach., Comment: Accepted to Intelligent Vehicles Symposium 2022

We study Chern-Simons theories at large $N$ with either bosonic or fermionic matter in the fundamental representation. The most fundamental operators in these theories are mesonic line operators, the simplest example being Wilson lines ending on fundamentals. We classify the conformal line operators along an arbitrary smooth path as well as the spectrum of conformal dimensions and transverse spins of their boundary operators at finite 't Hooft coupling. These line operators are shown to satisfy first-order chiral evolution equations, in which a smooth variation of the path is given by a factorized product of two line operators. We argue that this equation together with the spectrum of boundary operators are sufficient to uniquely determine the expectation values of these operators. We demonstrate this by bootstrapping the two-point function of the displacement operator on a straight line. We show that the line operators in the theory of bosons and the theory of fermions satisfy the same evolution equation and have the same spectrum of boundary operators., Comment: 12 pages, 3 figures. v2: typos corrected. v3: perturbative checks added; minor improvements. v4: minor improvements

Form factors in planar $\mathcal{N}=4$ super-Yang-Mills theory have a dual description in terms of periodic Wilson loops. This duality maps the multi-collinear expansion of the former to an operator product expansion of the latter. The coefficients of this expansion are decomposed in terms of several elementary building blocks and can be determined at finite 't Hooft coupling using bootstrap and integrability techniques. Some of these blocks are known from an analogous expansion of scattering amplitudes. In addition to these, the expansion for form factors includes a new type of building block, called {\it form factor transitions}, that encode information about the local operator. In the present paper, we consider the form factor of the chiral part of the stress-tensor supermultiplet. We bootstrap the corresponding form factor transitions of two-particle flux-tube states and use them to predict the leading term in the collinear expansion at finite coupling. The transitions we find can be expressed in terms of a quantity that previously appeared in a seemingly unrelated context, namely the octagon kernel. Lastly, we use a factorized ansatz to determine the multi-particle form factor transitions at finite coupling, which we use to predict the first subleading term in the collinear expansion. A perfect match is found between our predictions and the available perturbative data., Comment: 36 pages, 4 figures, v2: typos fixed and a reference added, matches published version

We consider the $2\to 2$ scattering amplitude of identical massive particles. We identify the Landau curves in the multi-particle region $16m^2 \leq s, t < 36m^2$. We systematically generate and select the relevant graphs and numerically solve the associated Landau equations for the leading singularity. We find an infinite sequence of Landau curves that accumulates at finite $s$ and $t$ on the physical sheet. We expect that such accumulations are generic for $s,t > 16m^2$. Our analysis sheds new light on the complicated analytic structure of nonperturbative relativistic scattering amplitudes., Comment: 9 pages + appendices, 28 figures

We consider a dual $S$-matrix Bootstrap approach in $d\geq 3$ space-time dimensions which relies solely on the rigorously proven analyticity, crossing, and unitarity properties of the scattering amplitudes. As a proof of principle, we provide rigorous upper and lower numerical bounds on the quartic coupling for the scattering of identical scalar particles in four dimensions., Comment: 5 + 10 pages, 3 + 6 figures, major revision in the appendices, improved numerics, typos corrected

Many experts argue that the future of artificial intelligence is limited by the field's ability to integrate symbolic logical reasoning into deep learning architectures. The recently proposed differentiable MAXSAT solver, SATNet, was a breakthrough in its capacity to integrate with a traditional neural network and solve visual reasoning problems. For instance, it can learn the rules of Sudoku purely from image examples. Despite its success, SATNet was shown to succumb to a key challenge in neurosymbolic systems known as the Symbol Grounding Problem: the inability to map visual inputs to symbolic variables without explicit supervision ("label leakage"). In this work, we present a self-supervised pre-training pipeline that enables SATNet to overcome this limitation, thus broadening the class of problems that SATNet architectures can solve to include datasets where no intermediary labels are available at all. We demonstrate that our method allows SATNet to attain full accuracy even with a harder problem setup that prevents any label leakage. We additionally introduce a proofreading method that further improves the performance of SATNet architectures, beating the state-of-the-art on Visual Sudoku., Comment: Code available at https://github.com/SeverTopan/SATNet

Form factors in planar N=4 Super-Yang-Mills theory admit a type of non-perturbative operator product expansion (OPE), as we have recently shown in arXiv:2009.11297. This expansion is based on a decomposition of the dual periodic Wilson loop into elementary building blocks: the known pentagon transitions and a new object that we call form factor transition, which encodes the information about the local operator. In this paper, we compute the two-particle form factor transitions for the chiral part of the stress-tensor supermultiplet at Born level; they yield the leading contribution to the OPE. To achieve this, we explicitly construct the Gubser-Klebanov-Polyakov two-particle singlet states. The resulting transitions are then used to test the OPE against known perturbative data and to make higher-loop predictions., Comment: 35 pages, 4 figures, 2 ancillary files; v2: LaTeX figure issue fixed

In this work, we propose a novel missile guidance algorithm that combines deep learning based trajectory prediction with nonlinear model predictive control. Although missile guidance and threat interception is a well-studied problem, existing algorithms' performance degrades significantly when the target is pulling high acceleration attack maneuvers while rapidly changing its direction. We argue that since most threats execute similar attack maneuvers, these nonlinear trajectory patterns can be processed with modern machine learning methods to build high accuracy trajectory prediction algorithms. We train a long short-term memory network (LSTM) based on a class of simulated structured agile attack patterns, then combine this predictor with quadratic programming based nonlinear model predictive control (NMPC). Our method, named nonlinear model based predictive control with target acceleration predictions (NMPC-TAP), significantly outperforms compared approaches in terms of miss distance, for the scenarios where the target/threat is executing agile maneuvers., Comment: Accepted for the 2021 American Control Conference (ACC)

Non-volatile magnetic storage, from 1940s magnetic core to present day racetrack memory and magnetic anisotropy switching devices rely on the metastability of magnetic domains to store information. However, the inherent inefficiency of converting the information-carrying charge current into magnetization switching sets fundamental limitations in energy consumption. Other non-magnetic non-volatile memories such as memristors, ferroelectric memory and phase change memory devices also rely on energetically relatively costly crystal structural rearrangements to store information. In contrast, conventional electronic charge states in quantum dots for example, can be switched in femtoseconds with high efficiency, but any stored information dissipates rapidly. Here we present a radically different approach in the form of a charge-configuration memory (CCM) device that relies on charge-injection-driven electronic crystal melting and topological protection of the resulting electronic domain configurations of a two-dimensional electronic crystal to store information. With multiprobe scanning tunneling microscopy (STM) we show microscopically, within an operational device, how dislocations in the domain ordering lead to metastability by a mechanism that is topologically equivalent to magnetic bubble memory. The devices have a very small switching energy (<2.2 fJ/bit), ultrafast switching speed of <11 ps and operational range over more than 3 orders of magnitude in temperature (<250 mK ~ 190 K). Together with their simple functionality, a large resistance switching ratio, straightforward fabrication and impressive endurance, CCM devices introduce a new memory paradigm in emerging cryo-computing and other high-performance computing applications that require ultrahigh speed and low energy consumption., Comment: Submitted to Nature Electronics, 18.05.2020

We solve the Schr\"odinger equation for a charged particle in the non-uniform magnetic field by using the Nikiforov-Uvarov method. We find the energy spectrum and the wave function, and present an explicit relation for the partition function. We give analytical expressions for the thermodynamic properties such as mean energy and magnetic susceptibility, and analyze the entropy, free energy and specific heat of this system numerically. It is concluded that the specific heat and magnetic susceptibility increase with external magnetic field strength and different values of the non-uniformity parameter, $\alpha$, in the low temperature region, while the mentioned quantities are decreased in high temperature regions due to increasing the occupied levels at these regions. The non-uniformity parameter has the same effect with a constant value of the magnetic field on the behavior of thermodynamic properties. On the other hand, the results show that transition from positive to negative magnetic susceptibility depends on the values of non-uniformity parameter in the constant external magnetic field., Comment: 22 pages, 7 figures

We propose an operator product expansion for planar form factors of local operators in $\mathcal{N}=4$ SYM theory. This expansion is based on the dual conformal symmetry of these objects or, equivalently, the conformal symmetry of their dual description in terms of periodic Wilson loops. A form factor is decomposed into a sequence of known pentagon transitions and a new universal object that we call the "form factor transition". This transition is subject to a set of non-trivial bootstrap constraints, which we expect to be sufficient to fully determine it. We evaluate the form factor transition for MHV form factors of the chiral half of the stress tensor supermultiplet at leading order in perturbation theory and use it to produce OPE predictions at any loop order. We match the one-loop and two-loop predictions with data available in the literature., Comment: 7 pages, 5 figures. v2: references added, convention changed

The Deng-Fan-Eckart (DFE) potential is as good as the Morse potential in studying atomic interaction in diatomic molecules. By using the improved Pekeris-type approximation, to deal with the centrifugal term, we obtain the bound-state solutions of the radial Schr\"odinger equation with this adopted molecular model via the Factorization Method. With the energy equation obtained, the thermodynamic properties of some selected diatomic molecules(H2 , CO , and ScN ) were obtained using Poisson summation method.. The unnormalized wave function is also derived. The energy spectrum for a set of diatomic molecules for different values of the vibrational n and rotational l are obtained. To show the accuracy of our results, we discuss some special cases by adjusting some potential parameters and also compute the numerical eigenvalue of the Deng-Fan potential for comparison sake. However, it was found out that our results agree excellently with the results obtained via other methods., Comment: 29 pages, 18 figures, 4 tables, 4902 words

Some identities for noncommutative perspectives of operator monotone functions in Hilbert spaces aregiven. Applications for weighted operator geometric mean and relative operator entropy are also provided.

We obtain the quantized momentum eigenvalues, $P_n$, together with space-like coherent eigenstates for the space-like counterpart of the Schrodinger equation, the Feinberg-Horodecki equation, with a combined Kratzer potential plus screened coulomb potential which is constructed by temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: the time-dependent modified Kratzer potential and the time-dependent screened Coulomb potential., Comment: arXiv admin note: substantial text overlap with arXiv:2006.12295, arXiv:2007.13836, arXiv:2007.14789

We revisit analytical methods for constraining the nonperturbative $S$-matrix of unitary, relativistic, gapped theories in $d \geq 3$ spacetime dimensions. We assume extended analyticity of the two-to-two scattering amplitude and use it together with elastic unitarity to develop two natural expansions of the amplitude. One is the threshold (non-relativistic) expansion and the other is the large spin expansion. The two are related by the Froissart-Gribov inversion formula. When combined with crossing and a local bound on the discontinuity of the amplitude, this allows us to constrain scattering at finite energy and spin in terms of the low-energy parameters measured in the experiment. Finally, we discuss the modern numerical approach to the $S$-matrix bootstrap and how it can be improved based on the results of our analysis., Comment: 83 pages, 14 figures

In this paper we obtain some operator versions of Levin-Steckin integral inequality.

GipsyX/RTGx is the Jet Propulsion Laboratory's (JPL) next generation software package for positioning, navigation, timing, and Earth science using measurements from three geodetic techniques: Global Navigation Satellite Systems (GNSS), Satellite Laser Ranging (SLR), and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS); with Very Long Baseline Interferometry (VLBI) under development. The software facilitates combined estimation of geodetic and geophysical parameters using a Kalman filter approach on real or simulated data in both post-processing and in real-time. The estimated parameters include station coordinates and velocities, satellite orbits and clocks, Earth orientation, ionospheric and tropospheric delays. The software is also capable of full realization of a dynamic terrestrial reference through analysis and combination of time series of ground station coordinates. We present some key aspects of its new architecture, and describe some of its major applications, including Real-time orbit determination and ephemeris predictions in the U.S. Air Force Next Generation GPS Operational Control Segment (OCX), as well as in JPL's Global Differential GPS (GDGPS) System, supporting User Range Error (URE) of $<$ 5 cm RMS; precision post-processing GNSS orbit determination, including JPL's contributions to the International GNSS Service (IGS) with URE in the 2 cm RMS range; Precise point positioning (PPP) with ambiguity resolution, both statically and kinematically, for geodetic applications with 2 mm horizontal, and 6.5 mm vertical repeatability for static positioning; Operational orbit and clock determination for Low Earth Orbiting (LEO) satellites, such as NASA's Gravity Recovery and Climate Experiment (GRACE) mission with GRACE relative clock alignment at the 20 ps level., Comment: 65 pages, 14 figures

We introduce a new class of operators in any theory with a 't Hooft large-$N$ limit that we call colour-twist operators. They are defined by twisting the colour-trace with a global symmetry transformation and are continuously linked to standard, un-twisted single-trace operators. In particular, correlation functions between operators that are twisted by an R-symmetry of ${\cal N}=4$ SYM extend those in the $\gamma$-deformed theory. The most general deformation also breaks the Lorentz symmetry but preserves integrability in the examples we consider. In this paper, we focus on colour-twist operators in the fishnet model. We exemplify our approach for the simplest colour-twist operators with one and two scalar fields, which we study non-perturbatively using field-theoretical as well as integrability methods, finding a perfect match. We also propose the quantisation condition for the Baxter equation appearing in the integrability calculation in the fishnet model. The results of this paper constitute a crucial step towards building the separation of variable construction for the correlation functions by means of the Quantum Spectral Curve approach., Comment: 66 pages, 20 figures

In this research work, the Hellmann potential is studied in the presence of external magnetic and AB-flux fields. We solve the Schrodinger in the presence of these fields and the potential via the functional analysis approach (FAA). The energy equation and wave function of the system are obtained in closed form. The effect of the fields on the energy spectra of the system examined in details. It is found that the AB field performs better than the magnetic in its ability to remove degeneracy. Furthermore, the magnetization and magnetic susceptibility of the system was discussed at zero and finite temperatures. We evaluate the partition function and use it to evaluate other thermodynamic properties of the system such as magnetic susceptibility, Helmholtz free energy,entropy, internal energy and specific heat. A comparative analysis of the magnetic susceptibility of the system at zero and finite temperature shows a similarity in the behavior of the system. A straight forward extension of our results to three dimension shows that the present result is consistent with what is obtains in literature., Comment: 34 pages, 32 Figures

In this work, the thermodynamic property of pseudoharmonic potential in the presence of external magnetic and AB fields is investigated. We used effective Boltzmann factor within the superstatistics formalism to obtain the thermodynamic properties such as Helmholtz free energy (F), Internal energy (U), entropy(S) and specific heat (C) of the system. In addition, we discuss the result of the thermodynamic properties of some selected diatomic molecules of N2, Cl2, I2 and CH using their experimental spectroscopic parameters and that of the variation of the deformation parameter of q=0,0.3,0.7. We also illustrated with some graphs for clarity of our results in both cases., Comment: 25 pages, 15 figures

Recently, we constructed the first-principle derivation of the holographic dual of N=4 SYM in the double-scaled $\gamma$-deformed limit directly from the CFT side. The dual fishchain model is a novel integrable chain of particles in AdS5. It can be viewed as a discretized string and revives earlier string-bit approaches. The original derivation was restricted to the operators built out of one of two types of scalar fields. In this paper, we extend our results to the general operators having any number of scalars of both types, except for a very special case when their numbers are equal. Interestingly, the extended model reveals a new discrete reparametrization symmetry of the "world-sheet", preserving all integrals of motion. We use integrability to formulate a closed system of equations, which allows us to solve for the spectrum of the model in full generality, and present non-perturbative numerical results. We show that our results are in agreement with the Asymptotic Bethe Ansatz of the fishnet model up to the wrapping order at weak coupling., Comment: 30 pages, 11 figures. v2: references added

In our previous paper we derived the holographic dual of the planar fishnet CFT in four dimensions. The dual model becomes classical in the strongly coupled regime of the CFT and takes the form of an integrable chain of particles in five dimensions. Here we study the theory at the quantum level. By applying the canonical quantization procedure with constraints, we show that the model describes a quantum chain of particles propagating in $AdS_5$. We prove the duality at the full quantum level in the ${\mathfrak u}(1)$ sector and reproduce exactly the spectrum for the cases when it is known analytically., Comment: 38 pages, 3 figures, v2 - typos corrected, references updated, v3 - acknowledgment added

We solve the Schr\"odinger wave equation for the generalized Morse and Cusp molecular potential models. In the limit of high temperature, at first, we need to calculate the canonical partition function which is basically used to study the behavior of the thermodynamic functions. Based on this, we further calculate the thermodynamic quantities such as the free energy, the entropy, the mean energy and the specific heat. Their behavior with the temperature has been investigated. In addition, the susceptibility for two level systems is also found by applying the incident time dependent field., Comment: 6 Figures

We present the first-principle derivation of a weak-strong duality between the fishnet theory in four dimensions and a discretized string-like model living in five dimensions. At strong coupling, the dual description becomes classical and we demonstrate explicitly the classical integrability of the model. We test our results by reproducing the strong coupling limit of the $4$-point correlator computed before non-perturbatively from the conformal partial wave expansion. Due to the extreme simplicity of our model, it could provide an ideal playground for holography with no super-symmetry. Furthermore, since the fishnet model and ${\cal N}=4$ SYM theory are continuously linked our consideration could shed light on the derivation of AdS/CFT for the latter., Comment: 5 pages. v2: references added, v3 - acknowledgment added

In this paper, obtained some new class of Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities via fractional integrals for the p-hyperbolic convex functions. It is shown that such inequalities are simple consequences of Hermite-Hadamard-Fejer inequality for the p-hyperbolic convex function., Comment: 11 pages

We present exact analytical solutions of the Dirac equation in $(1+1)$-dimensions for the generalized Kratzer potential by taking the pseudoscalar interaction term as an attractive Coulomb potential. We study the problem for a particular (spin) symmetry of the Dirac Hamiltonian. After a qualitative analyse, we study the results for some special cases such as Dirac-Coulomb problem in the existence of the pseudoscalar interaction, and the "pure" Coulomb problem by discussing some points about pseudospin and spin symmetries in one dimension. We also plot some figures representing the dependence of the energy on quantum number, and potential parameters., Comment: 18 pages, 3 figures

We present several operator extensions of the Chebyshev inequality for Hilbert space operators. The main version deals with the synchronous Hadamard property for Hilbert space operators. Among other inequalities, it is shown that if ${\mathfrak A}$ is a $C^*$-algebra, $T$ is a compact Hausdorff space equipped with a Radon measure $\mu$ as a totaly order set, then \begin{align*} \int_{T} \alpha(s) d\mu(s)\int_{T}\alpha(t)(A_t\circ B_t) d\mu(t)\geq\Big{(}\int_{T}\alpha(t) (A_tm_{r,\alpha} B_t) d\mu(t)\Big{)}\circ\Big{(}\int_{T}\alpha(s) (A_sm_{r,1-\alpha} B_s) d\mu(s)\Big{)}, \end{align*} where $\alpha\in[0,1]$, $r\in[-1,1]$ and $(A_t)_{t\in T}, (B_t)_{t\in T} $ are positive increasing fields in $\mathcal{C}(T,\mathfrak A)$., Comment: to appear in Azerbaijan Journal of Mathematics

We study the first non-planar correction to gluon scattering amplitudes in ${\cal N}=4$ SYM theory. The correction takes the form of a double trace partial amplitude and is suppressed by one power of $1/N$ with respect to the leading single trace contribution. We extend the duality between planar scattering amplitudes and null polygonal Wilson loops to the double trace amplitude. The new duality relates the amplitude to the correlation function of two infinite null polygonal Wilson lines that are subject to a quantum periodicity constraint. We test the duality perturbatively at one-loop order and demonstrate it for the dual string in AdS. The duality allows us to extend the notion of the loop integrand beyond the planar limit and to determine it using recursion relations. It also allows one to apply the integrability-based pentagon operator product expansion approach to the first non-planar order., Comment: 50 pages, 17 figures. v2 : typos corrected

In this paper we introduce the hypo-q-norms on a Cartesian product of normed linear spaces. A representation of these norms in terms of bounded linear functionals of norm less than one, the equivalence with the q-norms on a Cartesian product and some reverse inequalities obtained via the scalar Shisha-Mond, Birnacki et al. and other Gruss type inequalities are also given.

We need to solve a suitable exponential form of the position-dependent mass (PDM) Schr\"odinger equation with a charged particle placed in the Hulthen plus Coulomb-like potential field and under the influence of the external magnetic and Aharonov-Bohm (AB) flux fields. The bound state energies and their corresponding wave functions are calculated for spatially-dependent mass distribution function of a physical interest. A few plots of some numerical results to the energy are shown., Comment: 8 pages, 8 figures, Chinese Physics B (2017)

Some improvements of the celebrated Schwarz inequality in complex inner product spaces are given. Applications for n-tuples of complex numbers are provided.

We consider theories of weakly interacting higher spin particles in flat spacetime. We focus on the four-point scattering amplitude at high energies and imaginary scattering angles. The leading asymptotic of the amplitude in this regime is universal and equal to the corresponding limit of the Veneziano amplitude. In this paper, we find that the first sub-leading correction to this asymptotic is universal as well. We compute the correction using a model of relativistic strings with massive endpoints. We argue that it is unique using holography, effective theory of long strings and bootstrap techniques., Comment: 54 pages, 5 figures

We obtain the quantized momentum solutions, $\mathcal{P}_{n}$, of the Feinberg-Horodecki equation. We study the space-like coherent states for the space-like counterpart of the Schr\"odinger equation with trigonometric P\"oschl-Teller potential which is constructed by temporal counterpart of the spatial P\"oschl-Teller potential., Comment: 8 pages

We establish in this paper some inequalities for analytic and convex functions on an open interval and positive normalized functionals defined on a Hermitian unital Banach *-algebra. Reverses and refinements of Jensen's and Slater's type inequalities are provided. Some examples for particular convex functions of interest are given as well.

We investigate the energy spectrum and the corresponding eigenfunctions of a 2D Dirac oscillator confined by an antidot potential in the presence of a magnetic field and Aharonov-Bohm flux field. Analytical solutions are obtained and compared with the results of the Schr\"odinger equation found in the literature. Further, the dependence of the spectrum on the magnetic quantum number and on the repulsive potential is discussed., Comment: 12 pages

In this paper we introduce the quadratic weighted geometric mean for invertible elements x, y in a Hermitian unital Banach star-algebra and provide some inequalities for this mean under various assumptions for the elements involved., Comment: 15 pages