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In this paper, we focused on the study of anisotropic strange stars with anisotropic matter distribution in the framework of f ( T , T ) = α T ( r ) 2 + β T ( r ) model, where α , β are arbitrary constants, T and T represent the torsion scalar and trace of energy–momentum tensor, respectively. This model has interesting cosmological properties, in addition to providing an effective dark energy sector explanation (Harko et al., 2014). In order to achieve our goal, we considered the Krori-Barua space–time and utilize the off-diagonal tetrad components for deriving the corresponding set of field equations. We calculate the relation for the evaluation of effective density, effective radial and tangential pressure using the EoS of strange star i.e., MIT bag model p r ( r ) = 1 3 [ ρ ( r ) − 4 B g ] . The unknown constants appearing in the solution have been evaluated by using the conventional matching of interior and exterior space time. To check the feasibility of our proposed model we discuss the anisotropy, energy condition, TOV forces, abreu condition, EoS parameters, adiabatic index, mass function, compactness and redshift for different compact stars models namely, P S R J 1416 − 2230 , 4 U 1608 − 52 , C e n X − 3 , E X O 1785 − 248 and S M C X − 1 .

Morse complexes are gradient-based topological descriptors with close connections to Morse theory. They are widely applicable in scientific visualization as they serve as important abstractions for gaining insights into the topology of scalar fields. Data uncertainty inherent to scalar fields due to randomness in their acquisition and processing, however, limits our understanding of Morse complexes as structural abstractions. We, therefore, explore uncertainty visualization of an ensemble of 2D Morse complexes that arises from scalar fields coupled with data uncertainty. We propose several statistical summary maps as new entities for quantifying structural variations and visualizing positional uncertainties of Morse complexes in ensembles. Specifically, we introduce three types of statistical summary maps – the probabilistic map, the significance map, and the survival map – to characterize the uncertain behaviors of gradient flows. We demonstrate the utility of our proposed approach using wind, flow, and ocean eddy simulation datasets.

A quasi-mixed-potential layered medium Green’s function (QMP-LMGF) is proposed for non-Galerkin surface integral equation (SIE) formulations in the modeling of homogeneous dielectric objects in layered medium. The formulation is derived based on the pilot vector potential approach. In this method, the field-type LMGF in the L-operator is decomposed into two parts, a “vector potential” term in a dyadic form, and a “scalar potential” term in a vector form, to represent the field components from current and charge sources, respectively. Since the proposed two potential terms (vector potential and scalar potential) do not satisfy the Lorenz gauge, we term them as quasi-mixed-potentials. The property of the two potentials is investigated to reveal that the proposed QMP-LMGF is compatible with the vector and scalar potentials in free space. Moreover, due to the continuity of the integration kernels across the interfaces, undesired line integrals are absent in the proposed QMP-LMGF when the objects are straddling different layers. Three popular non-Galerkin SIEs for dielectric objects in layered medium are studied, and the corresponding numerical results are demonstrated to validate the proposed method.

In this chapter, which is organized very much like Chapter 3, we present bifurcation conditions defining the simplest bifurcations of fixed points in n-dimensional discrete-time dynamical systems: the fold, the flip, and the Neimark-Sacker bifurcations. Then we study these bifurcations in the lowest possible dimension in which they can occur: the fold and flip bifurcations for scalar systems and the Neimark-Sacker bifurcation for planar systems. In Chapter 5 it will be shown how to apply these results to n-dimensional systems when n is larger than one or two, respectively.

In this paper, a new approach to time series classification is proposed. It transforms the scalar time series into a two-dimensional space of amplitude (time series values) and a change of amplitude (increment). Subsequently, it uses this representation to plot the data. One figure is produced for each time series. In consequence, the time series classification problem is converted into the visual pattern recognition problem. This transformation allows applying a wide range of algorithms for standard pattern recognition – in this domain, there are more options to choose from than in the domain of time series classification. In this paper, we demonstrated the high effectiveness of the new method in a series of experiments on publicly available time series. We compare our results with several state-of-the-art approaches dedicated to time series classification. The new method is robust and stable. It works for time series of differing lengths and is easy to extend and alter. Even with a baseline variant presented in an empirical study in this paper, it achieves a satisfying classification accuracy. Furthermore, the proposed conversion of raw time series into images that are subjected to feature extraction opens the possibility to apply standard clustering algorithms.

A family of effective fully-discrete energy-preserving schemes for the space-fractional Klein–Gordon equation is developed in this paper. First, the recently developed Lagrange multiplier type scalar auxiliary variable approach is employed to obtain a new equivalent system from the original space-fractional Klein–Gordon system. Then, a family of special second-order implicit, explicit and implicit approximations to respectively discretize the linear parts, nonlinear parts and time-derivative parts are obtained in the above equivalent system to establish a family of semi-discrete (continuous in space) energy-preserving schemes. Furthermore, the Fourier pseudo-spectral method is used to discretize the space for extending to the fully-discrete case and rigorous theoretical proofs guarantee its conservation of original energy. Especially, the well-known implicit–explicit Crank–Nicolson type scheme is only one of the above-mentioned schemes. It is inspiring that the main computational efforts of this method in each time step are only to solve two linear, decoupled differential equations with constant coefficients different from non-homogeneous terms, which thus can be effectively solved. Finally, numerical experiments are carried out to verify the theoretical results of the accuracy, efficiency and conservation of original energy.

The diversity of magnetic field information obtained in marine geomagnetic measurements is of great relevance to defining detailed features of the targets. In this article, a solution algorithm based on the combination of scalar and vector fields is proposed. The magnetic direction of the geomagnetic field was obtained by repeatedly applying bias fields, and the multiparameter integrated measurement is realized based on the geometric relationship of the geomagnetic parameters. To make an instrument feasible for undersea measurement, a miniaturized multiparameter magnetometer was constructed within the limited space of a pressure tank, using an Overhauser scalar sensor and a spherical coil for generating bias fields. Test platforms were built to evaluate the scalar sensor and spherical coil. Results from a nonmagnetic laboratory showed that the expanded uncertainty of the scalar sensor was 0.11 nT, whereas the magnetic field generated by the spherical coil had 97% uniformity and completely engulfed the scalar sensor. Moreover, field experiments indicated that the standard deviation of prototype instrument in magnetic direction (3 $^{\prime \prime }$ ) was close to that of declination–inclination magnetometer, whereas its standard deviation in Z -component of 0.24 nT was better than that of a commercial fluxgate magnetometer. It also had markedly better measurement stability, with no temperature drift.

The fully parabolic cross-diffusion system { e u t = Δ u − χ ∇ ⋅ ( u v ∇ v ) , v t = Δ v − v + u , is considered under homogneous Neumann boundary conditions in a ball Ω ⊂ R n , n ≥ 1 , for e ∈ ( 0 , 1 ) and χ > 0 . Previous literature has asserted global existence of certain generalized solutions whenever χ n ( n − 2 ) + , but no result on any unboundedness phenomenon seems available; only in a parabolic-elliptic simplification, some solutions are known to blow up in finite time when n ≥ 3 and χ > 2 n n − 2 . The present study examines the solution behavior in the singular limit e ↘ 0 , and based on an essentially well-known result on finite-time blow-up in an accordingly obtained nonlocal scalar parabolic problem, under the assumptions that n ≥ 3 and χ > n n − 2 a statement on spontaneous emergence of arbitrarily large values of u for appropriately small e is derived.

The paper describes a novel method of sampled-data in space (spatial variable) nonlinear control of scalar semilinear parabolic and hyperbolic systems with unknown parameters, distributed disturbances and finite number of measurements along the spatial variable. Differently from recent results based on piecewise constant control laws, the proposed one is used piecewise nonlinear functions choosing by designer for providing some properties in the closed-loop system. In particular, we propose several types of functions providing reduced control. The gain design in the control law is found as a solution of linear matrix inequalities with minimum ultimate bound guarantee. The simulations confirm theoretical results and show the efficiency of the proposed control scheme compared with some existing ones.

In this study, we investigate black hole solutions with toroidal horizons in scalar hair and dilaton gravity. First, we obtain the field equations in n-dimensions. Then, we propose different models (ansatz) and find the exact solutions for these types of ansatzs. These solutions are not asymptotically (anti) de Sitter or flat, except in one special case. We also show that the BTZand BTZ-like solutions emerge from some of these solutions as a special case. We also show that when the event horizon radius increases, the temperature will be the same in various dimensions. The only difference is noticeable near the origin (this statement is clear from the figures). For these solutions, we obtained a new version of the Smarr formula. In addition, we show that the presence of the scalar field makes the black holes more stable near the origin, except for the BTZ case. In general, the presence of a scalar field is an important factor in black hole stability investigations. In the critical behavior analysis, we find that there is no evidence to show the existence of P-V criticality. Here, we present a class of interior solutions corresponding to the solution in a scalar hair gravity exterior. The solution obtained in the linear case was regular and well-behaved at the stellar interior.

The crucial step in elliptic curve scalar multiplication based on scalar decompositions using efficient endomorphisms—such as GLV, GLS or GLV+GLS—is to produce a short basis of a lattice involving the eigenvalues of the endomorphisms, which usually is obtained by lattice basis reduction algorithms or even more specialized algorithms. Recently, lattice basis reduction is found to be unnecessary. Benjamin Smith (AMS 2015) was able to immediately write down a short basis of the lattice for the GLV, GLS, GLV+GLS of quadratic twists using elementary facts about quadratic rings. Certainly it is always more convenient to use a ready-made short basis than to compute a new one by some algorithm. In this paper, we extend Smith's method on GLV+GLS for quadratic twists to quartic and sextic twists, and give ready-made short bases for $ 4 $-dimensional decompositions on these high degree twisted curves. In particular, our method gives a unified short basis compared with Hu et al.'s method (DCC 2012) for $ 4 $-dimensional decompositions on sextic twisted curves.

In this work we analyze how the spectrum of primordial scalar perturbations is modified, within the emergent universe scenario, when a particular version of the Continuous Spontaneous Localization (CSL) model is incorporated as the generating mechanism of initial perturbations, providing also an explanation to the quantum-to-classical transition of such perturbations. On the other hand, a phase of super-inflation, prior to slow-roll inflation, is a characteristic feature of the emergent universe hypothesis. In recent works, it was shown that the super-inflation phase could generically induce a suppression of the temperature anisotropies of the CMB at large angular scales. We study here under what conditions the CSL maintains or modifies these characteristics of the emergent universe and their compatibility with the CMB observations., Comment: 15 pages, 5 figures. Some references added. Version accepted in EPJC

In the present work the Chern-Simons(C-S) gauge field theory developed by Jackiw and Pi [1] and widely used to explain the fractional quantum Hall effects, was applied to describe the two-dimensional (2D) electron-hole (e-h) system in a strong perpendicular magnetic field under the influence of the quantum point vortices creating the Chern-Simons(C-S) gauge field. The composite particles formed by electrons and by holes with equal integer positive numbers of the attached quantum point vortices are described by the dressed field operators, which obey to the Fermi or to the Bose statistics depending on the even or odd numbers . It is shown that the phase operators as well as the vector and the scalar potentials of the C-S gauge field depend on the difference of the electron and of the hole density operators. They vanish in the mean field approximation, when the average values of the electron and of the whole densities coincide. Nevertheless, even in this case, the quantum fluctuations of the C-S gauge field lead to new physics of the 2D e-h system., 28 pages

In this paper we consider general multivector elements of Clifford algebras Cl(3,0), Cl(1,2) and Cl(0,3), and look for possibilities to factorize multivectors into products of blades, idempotents and exponentials, where the exponents are frequently blades of grades zero (scalar) to n (pseudoscalar).

This paper introduces the energy-preserving scheme for the nonlinear fractional Klein–Gordon Schrodinger equation, which uses the scalar auxiliary variable approach. By a scalar variable, the system is transformed into a new equivalent system. Then applying the extrapolated Crank–Nicolson method on the temporal direction and Fourier pseudospectral method on space direction, we give a linear implicit energy-preserving scheme. Moreover, it proved that at each discrete time the scheme preserves the corresponding discrete mass and energy. The unique solvability and convergence of the numerical solution are also investigated. In particular, it shows the method has the second-order accuracy in time and the spectral accuracy in space. Finally, it gives the algorithm implementation. Several numerical examples illustrate the efficiency and accuracy of the numerical scheme.

We apply a recently developed 2+1+1 decomposition of spacetime, based on a nonorthogonal double foliation for the study of spherically symmetric, static black hole solutions of Horndeski scalar-tensor theory. Our discussion proceeds in an effective field theory (EFT) of modified gravity approach, with the action depending on metric and embedding scalars adapted to the nonorthogonal 2+1+1 decomposition. We prove that the most generic class of Horndeski Lagrangians compatible with observations can be expressed in this EFT form. By studying the first order perturbation of the EFT action we derive three equations of motion, which reduce to those derived earlier in an orthogonal 2+1+1 decomposition, and a fourth equation for the metric parameter N related to the nonorthogonality of the foliation. For the Horndeski class of theories with vanishing $G_3$ and $G_5$, but generic functions $G_2(\phi,X)$ (k-essence) and $G_4(\phi)$ (nonminimal coupling to the metric) we prove the unicity theorem that no action beyond Einstein--Hilbert allows for the Schwarzschild solution. Next we integrate the EFT field equations for the case with only one independent metric function obtaining new solutions characterized by a parameter interpreted as either mass or tidal charge, the cosmological constant and a third parameter. These solutions represent naked singularities, black holes with scalar hair or have the double horizon structure of the Schwarzschild--de Sitter spacetime. Solutions with homogeneous Kantowski--Sachs type regions also emerge. Finally, one of the solutions obtained for the function $G_4$ linear in the curvature coordinate, in certain parameter range exhibits an intriguing logarithmic singularity lying outside the horizon. The newly derived hairy black hole solutions evade previously known unicity theorems by being asymptotically nonflat, even in the absence of the cosmological constant., Comment: 20 pages, 4 figures

This study aims to investigate adult L2 speakers’ use of different types of information in the comprehension of pragmatic inferences by examining L1-Mandarin Chinese L2-English speakers’ sensitivit...

We show a global in time Strichartz estimate for the isotropic Maxwell system with divergence free data. On the scalar permittivity and permeability we impose decay assumptions as $|x|\rightarrow\infty$ and a non-trapping condition. The proof is based on smoothing estmates in weighted $L^2$ spaces which follow from corresponding resolvent estimates for the underlying Helmholtz problem.

Fluorine atoms are known to display scalar 19F-19F couplings in nuclear magnetic resonance (NMR) spectra when they are sufficiently close in space for nonbonding orbitals to overlap. We show that fluorinated noncanonical amino acids positioned in the hydrophobic core or on the surface of a protein can be linked by scalar through-space 19F-19F (TSJFF) couplings even if the 19F spins are in the time average separated by more than the van der Waals distance. Using two different aromatic amino acids featuring CF3 groups, O-trifluoromethyl-tyrosine and 4-trifluoromethyl-phenylalanine, we show that 19F-19F TOCSY experiments are sufficiently sensitive to detect TSJFF couplings between 2.5 and 5 Hz in the 19 kDa protein PpiB measured on a two-channel 400 MHz NMR spectrometer with a regular room temperature probe. A quantitative J evolution experiment enables the measurement of TSJFF coupling constants that are up to five times smaller than the 19F NMR line width. In addition, a new aminoacyl-tRNA synthetase was identified for genetic encoding of N6-(trifluoroacetyl)-l-lysine (TFA-Lys) and 19F-19F TOCSY peaks were observed between two TFA-Lys residues incorporated into the proteins AncCDT-1 and mRFP despite high solvent exposure and flexibility of the TFA-Lys side chains. With the ready availability of systems for site-specific incorporation of fluorinated amino acids into proteins by genetic encoding, 19F-19F interactions offer a straightforward way to probe the spatial proximity of selected sites without any assignments of 1H NMR resonances.

Purpose The aim of this study is to examine the scalar dislocation rate in straight and perimodiolar electrode arrays in relation to cochlear morphology. Furthermore, we aim to analyze the specific dislocation point of electrode arrays depending on their design and shape and to correlate these results to postoperative speech perception. Methods We conducted a comparative analysis of patients (ears: n = 495) implanted between 2013 and 2018 with inserted perimodiolar or straight electrode arrays from Cochlear™ or MED-EL. CBCT (cone beam computed tomography) was used to determine electrode array position (scalar insertion, intra-cochlear dislocation, point of dislocation and angular insertion depth). Furthermore, cochlear morphology was measured. The postoperative speech discrimination was compared regarding electrode array dislocation, primary scalar insertion and angular insertion depth. Results The electrode array with the highest rate of primary SV insertions was the CA; the electrode array with the highest rate of dislocations out of ST was the FlexSoft. We did not find significantly higher dislocation rates in cochleostomy-inserted arrays. The angle of dislocation was electrode array design-specific. A multivariate nonparametric analysis revealed that the dislocation of the electrode array has no significant influence on postoperative speech perception. Nevertheless, increasing angular insertion depth significantly reduced postoperative speech perception for monosyllables. Conclusion This study demonstrates the significant influence of electrode array design on scalar location, dislocation and the angle of dislocation itself. Straight and perimodiolar electrode arrays differ from each other regarding both the rate and place of dislocation. Insertion via cochleostomy does not lead to increased dislocation rates in any of the included electrode arrays. Furthermore, speech perception is significantly negatively influenced by angular insertion depth.

Many models of damage or cracking of isotropic solids consider a single damage/crack density variable. Based on both continuum damage mechanics (CDM) and effective medium theory (EMT), we model the impact of isotropic damage in the form of microcracks on the elastic properties of an isotropic solid. For each approach, we consider the complete tensorial description of the elastic moduli involving two damage/crack density variables $$D_{1}$$ and $$D_{2}$$ , or $$\alpha$$ and $$\beta$$ ; and possible scalar approximations involving a single variable (with either $$D_{2}$$ = 0, or $$\beta$$ = 0). We assess the accuracy of scalar approximations commonly employed for each approach against laboratory measurements of ultrasonic wave velocities and density obtained on a dry and isotropic specimen of thermally cracked Carrara Marble (CM) subjected to an increasing confining pressure up to 50 MPa. Overall, this laboratory dataset and the CDM and EMT modelling and inversion results reported here suggest that: (i) irreversible thermal cracking and microcrack opening occur after heating and sudden cooling of the CM specimen, whereas reversible and progressive microcracks’ closure occurs with increasing confining pressure; (ii) tensorial damage/cracking models involving either two damage variables (CDM) or two crack density variables (EMT) fit equally well and virtually perfectly the laboratory data for any confining pressure tested; (iii) single scalar approximation models commonly used in CDM or the EMT models give comparable results to their complete tensorial counterparts, which is particularly true for the CDM approach; (iv) single scalar approximations derived from the CDM approach, and assuming a constant Poisson’s ratio of the cracked rock, reproduces all the elastic moduli more accurately than the corresponding scalar approximation derived from the EMT approach, where a constant ratio of Young’s modulus to Poisson’s ratio is assumed instead; and (v) it is more reliable to use a tensorial rather than a scalar description of the effect of reversible microcrack closure with pressure on all elastic parameters, including Poisson’s ratio. If the impact of reversible microcrack closure is accounted for, then a single scalar description of irreversible thermal damage with the CDM approach is remarkably accurate.

Using a Banach manifold structure on the space of finite positive measures it is shown that all critical points of the Gibbs/information entropy are grand canonical equilibria when the constraints are scalar, and local equilibria when the constraints are integrable functions. This provides a rigorous derivation of equilibrium and local equilibrium Gibbs measures via Lagrange multipliers.

In the linguistics literature, the derivation of scalar implicatures has often been handled in a relatively modular way, using computations that are sensitive to logical relations among alternatives such as entailment but are blind to other notions such as the probabilities that participants in a conversation might associate with these alternatives (or with related propositions). In recent years, a family of models that we refer to as iterated rationality models (IRMs) have offered an interestingly different perspective on such alternative-sensitive processes in terms of multiple iterations of (typically probabilistic) reasoning. Our paper investigates what at first sight seems like a very interesting argument for the adequacy of IRMs as models of scalar implicatures, coming from the conjunctive interpretation of disjunctive sentences. We then outline challenges for the argument based on a theoretical comparison with the grammatical theory of scalar implicatures. The comparison focuses on the full distribution of conjunctive interpretation, on the question of sensitivity to priors, and on other results achieved within the grammatical theory that the IRM literature has yet to engage with.

We propose a minimal model that can explain the electroweak scale, neutrino masses, Dark Matter (DM), and successful inflation all at once based on the multicritical-point principle (MPP). The model has two singlet scalar fields that realize an analogue of the Coleman-Weinberg mechanism, in addition to the Standard Model with heavy Majorana right-handed neutrinos. By assuming a $Z_2 $ symmetry, one of the scalars becomes a DM candidate whose property is almost the same as the minimal Higgs-portal scalar DM. In this model, the MPP can naturally realize a saddle point in the Higgs potential at high energy scales. By the renormalization-group analysis, we study the critical Higgs inflation with non-minimal coupling $\xi |H|^2 R$ that utilizes the saddle point of the Higgs potential. We find that it is possible to realize successful inflation even for $\xi=25$ and that the heaviest right-handed neutrino is predicted to have a mass around $10^{14}$ GeV to meet the current cosmological observations. Such a small value of $\xi$ can be realized by the Higgs-portal coupling $\lambda_{SH}\simeq 0.32$ and the vacuum expectation value of the additional neutral scalar $\langle\phi\rangle\simeq 2.7$ TeV, which correspond to the dark matter mass 2.0 TeV, its spin-independent cross section $1.8\times10^{-9}$ pb, and the mass of additional neutral scalar 190 GeV., Comment: 30 pages, 7 figures; Version accepted in EPJC (v2)

We study a mathematical relationship between holographic Wilsonian renormalization group and stochastic quantization framework. We extend the original proposal given in arXiv:1209.2242 to interacting theories. The original proposal suggests that fictitious time(or stochastic time) evolution of stochastic 2-point correlation function will be identical to the radial evolution of the double trace operator of certain classes of holographic models, which are free theories in AdS space. We study holographic gravity models with interactions in AdS space and establish a map between the holographic renormalization flow of multi-trace operators and stochastic $n$-point functions. To give precise examples, we extensively study conformally coupled scalar theory in AdS$_6$. What we have found is that the stochastic time $t$ dependent 3-point function obtained from Langevin equation with its Euclidean action being given by $S_E=2I_{os}$ is identical to holographic renormalization group evolution of holographic triple trace operator as its energy scale $r$ changes once an identification of $t=r$ is made. $I_{os}$ is the on-shell action of holographic model of conformally coupled scalar theory at the AdS boundary. We argue that this can be fully extended to mathematical relationship between multi point functions and multi trace operators in each framework., Comment: 1+23 pages

In this paper, we study the spontaneous scalarization of Reissner-Nordstr{\"o}% m (RN) black holes enclosed by a cavity in an Einstein-Maxwell-scalar (EMS) model with non-minimal couplings between the scalar and Maxwell fields. In this model, scalar-free RN black holes in a cavity may induce scalarized black holes due to the presence of a tachyonic instability of the scalar field near the event horizon. We calculate numerically the black hole solutions, and investigate the domain of existence, perturbative stability against spherical perturbations and phase structure. The scalarized solutions in a cavity are always thermodynamically preferred over scalar-free solutions. In addition, a reentrant phase transition, composed of a zeroth-order phase transition and a second-order one, occurs for large enough electric charge $Q$., Comment: arXiv admin note: text overlap with arXiv:2012.01066, arXiv:2102.04015 by other authors

We study 2-point correlation functions for scalar operators in position space through holography including bulk cubic couplings as well as higher curvature couplings to the square of the Weyl tensor. We focus on scalar operators with large conformal dimensions. This allows us to use the geodesic approximation for propagators. In addition to the leading order contribution, captured by geodesics anchored at the insertion points of the operators on the boundary and probing the bulk geometry thoroughly studied in the literature, the first correction is given by a Witten diagram involving both the bulk cubic coupling and the higher curvature couplings. As a result, this correction is proportional to the VEV of a neutral operator $O_k$ and thus probes the interior of the black hole exactly as in the case studied by Grinberg and Maldacena [13]. The form of the correction matches the general expectations in CFT and allows to identify the contributions of $T^nO_k$ (being $T^n$ the general contraction of n energy-momentum tensors) to the 2-point function. This correction is actually the leading term for off-diagonal correlators (i.e. correlators for operators of different conformal dimension), which can then be computed holographically in this way., Comment: 23 pages

Secure scalar product computation is a special secure multi-party computation problem. A secure scalar product protocol can be used by two parties to jointly compute the scalar product of their private vectors without revealing any information about the private vector of either party. Secure scalar product protocol is of great significance in privacy-preserving scientific computing, privacy preserving data mining, privacypreserving cooperative statistical analysis and privacypreserving geometry computation, etc. Many privacy preserving computing problems can be transformed to secure scalar product computation. At present, existing scalar product protocols cannot be used to privately compute scalar product of private vectors with both positive and negative components. Based on homomorphic encryption scheme, we design three protocols to compute scalar product of three different kinds of private vectors. The components of the first kind vector are arbitrary integers; those of the second kind are positive rational numbers and those of the third kind are arbitrary rational numbers. We use simulation paradigm proving that the protocols are secure in the semi-honest model. Theoretical analysis and experimental results show that the protocols designed in this paper are efficient.

We provide a systematic method to compute tree-level scattering amplitudes with spinning external states from amplitudes with scalar external states in arbitrary spacetime dimensions. We write down analytic answers for various scattering amplitudes, including the four graviton amplitude due to the massive spin $J$ exchange. We verify the results by computing angular distributions in 3 + 1 dimensions using various identities involving Jacobi polynomials., Textual improvements, updated bibliography. Version to appear in JHEP

The problem of secure distributed batch matrix multiplication (SDBMM) studies the communication efficiency of retrieving a sequence of desired matrix products ${\bf AB}$ $=$ $({\bf A}_1{\bf B}_1,$ ${\bf A}_2{\bf B}_2,$ $\cdots,$ ${\bf A}_S{\bf B}_S)$ from $N$ distributed servers where the constituent matrices ${\bf A}=({\bf A}_1, {\bf A}_2, \cdots, {\bf A}_S)$ and ${\bf B}=({\bf B}_1, {\bf B}_2,\cdots,{\bf B}_S)$ are stored in $X$-secure coded form, i.e., any group of up to $X$ colluding servers learn nothing about ${\bf A, B}$. It is assumed that ${\bf A}_s\in\mathbb{F}_q^{L\times K}, {\bf B}_s\in\mathbb{F}_q^{K\times M}, s\in\{1,2,\cdots, S\}$ are uniformly and independently distributed and $\mathbb{F}_q$ is a large finite field. The rate of an SDBMM scheme is defined as the ratio of the number of bits of desired information that is retrieved, to the total number of bits downloaded on average. The supremum of achievable rates is called the capacity of SDBMM. In this work we explore the capacity of SDBMM, as well as several of its variants, e.g., where the user may already have either ${\bf A}$ or ${\bf B}$ available as side-information, and/or where the security constraint for either ${\bf A}$ or ${\bf B}$ may be relaxed. We obtain converse bounds, as well as achievable schemes for various cases of SDBMM, depending on the $L, K, M, N, X$ parameters, and identify parameter regimes where these bounds match. A remarkable aspect of our upper bounds is a connection between SDBMM and a form of private information retrieval (PIR) problem, known as multi-message $X$-secure $T$-private information retrieval (MM-XSTPIR). Notable features of our achievable schemes include the use of cross-subspace alignment and a transformation argument that converts a scalar multiplication problem into a scalar addition problem, allowing a surprisingly efficient solution., The updated version is the revision for IEEE IT Transactions

In this paper, we establish Parseval identities and surprising new inequalities for weaving frames in Hilbert spaces which involve scalar $\lambda \in {\mathcal{R}}$ λ ∈ R . With suitable choices of λ, one obtains the previous results as special cases. Our results generalize and improve the remarkable results obtained by Balan et al. and Găvruţa.

The paper deals with the reliable solution to the homogenization problem for the scalar heat equation with the uncertain hysteresis Prandtl–Ishlinskii operator. The problem is solved by the so-called worst scenario method. The contribution extends the results of paper Franců (2017), to the corresponding homogenization problem.

A scalar-relativistic DFT study of isoelectronic, quadruple-bonded Group 6 metalloporphyrins (M = Mo, W) and Group 7 metallocorroles (M = Tc, Re) has uncovered dramatic differences in ionization potential (IP) and electron affinity (EA) among the compounds. Thus, both the IPs and EAs of the corrole derivatives are 1 eV or more higher than those of the porphyrin derivatives. These differences largely reflect the much lower orbital energies of the δ- and δ*-orbitals of the corrole dimers relative to those of the porphyrin dimers, which in turn reflect the higher (+III as opposed to +II) oxidation states of the metals in the former compounds. Significant differences have also been determined between Mo and W porphyrin dimers and between Tc and Re corrole dimers. These differences are thought to largely reflect greater relativistic destabilization of the 5d orbitals of W and Re relative to the 4d orbitals of Mo and Tc. The calculated differences in IP and EA should translate to major differences in electrochemical redox potentials-a prediction that in our opinion is well worth confirming.

Bounds on the spectrum of Schur complements of subdomain stiffness matrices with respect to the interior variables are key ingredients of the convergence analysis of FETI (finite element tearing and interconnecting) based domain decomposition methods. Here we give bounds on the regular condition number of Schur complements of ‘floating’ clusters arising from the discretization of 3D Laplacian on a cube decomposed into cube subdomains. The results show that the condition number of the cluster defined on a fixed domain decomposed into m × m × m cube subdomains connected by face and optionally edge averages increases proportionally to m. The estimates support scalability of unpreconditioned H-FETI-DP (hybrid FETI dual-primal) method. Though the research is most important for the solution of variational inequalities, the results of numerical experiments indicate that unpreconditioned H-FETI-DP with large clusters can be useful also for the solution of huge linear problems.

Vertical profiles of temperature, water vapour, and carbon dioxide ( $$\mathrm {CO}_{2}\,$$ ) densities are analyzed, together with the respective turbulent fluxes of these scalars during 9 nights when there was a consistent wind decay along the period, with a corresponding stable boundary layer regime transition from weak to very stable. The purpose is to understand whether the vertical gradients and fluxes of these scalars respond differently to the mean wind decay. A multi-resolution spectral decomposition is used to address how the patterns found depend on their temporal scale. Case studies show that only water vapour gradients and latent heat fluxes switch sign along the nights. The signs of sensible heat and $$\mathrm {CO}_{2}\,$$ fluxes on low-frequency scales oppose those on turbulent time scales, while the same does not always occur for latent heat. The covariance between fluctuations of temperature and those of both water vapour and $$\mathrm {CO}_{2}\,$$ are also analyzed, along with their spectral decompositions. Their role in the corresponding scalar flux budgets is evaluated by comparing two relevant terms in the budget equations. It is found that the term related to the vertical gradient exceeds the one related to the temperature–scalar covariance for wind speeds above a threshold, which is larger for latent heat flux than for both sensible heat and $$\mathrm {CO}_{2}\,$$ fluxes. The implications of this result for flux parametrizations are addressed.

Under investigation in this paper is the generalized AB system, which is extended from the well-known AB system that is used to describe the evolution of the wave packets in a marginally stable or unstable baroclinic shear flow. Introducing an auxiliary function $$\alpha (\tau )$$ , we construct the Nth-order vector solitary waves for the generalized AB system, which are different from the regular vector solitary waves in the existing literature. We find that the vector solitary waves are subject to spatiotemporal distortion (SD) effects in the evolution. Influenced by the SD effects, the vector solitary waves would evolve with the shape changes or the appearances, splits, combinations and disappearances of certain bulges. It is revealed that the SD effects do not change the interaction properties of the vector solitary waves. Excluding from the SD effects, we find that the interacting vector solitary waves not only exhibit the same local and global oscillations as the scalar solitary waves of AB system, but also lead to certain unique inelastic interactions as they possess different velocities. It is also found that two vector solitary waves with the same velocity may degenerate into a parallel-state solitary wave while two scalar solitary waves can not. For the interactions among the multi vector solitary waves, we observe that the symmetric parallel-state solitary waves interacting with standard bell-shaped solitary waves may bring about the destruction of the symmetric structures as well as the generation of the bound-state solitary waves, and that two symmetric parallel-state solitary waves interacting with each other may cause the broken symmetric structures for both ones. Moreover, the vector breathers and rogue waves of the generalized AB system are presented. Taking vector rogue waves in consideration, we demonstrate that the SD effects manifest themselves in two aspects: one is the destruction of the conventional one-peak-two-valley or four-petal symmetric structure; the other is the split of the rogue wave into some small ones with the adjustable number. Besides, modulation instability analysis presents the conditions under which the perturbed plane waves can develop into the distorted rogue waves.

Let T be a square matrix with a real spectrum, and let f be an analytic function. The problem of the approximate calculation of f(T) is discussed. Applying the Schur triangular decomposition and the reordering, one can assume that T is triangular and its diagonal entries tii are arranged in increasing order. To avoid calculations using the differences tii − tjj with close (including equal) tii and tjj, it is proposed to represent T in a block form and calculate the two main block diagonals using interpolating polynomials. The rest of the f(T) entries can be calculated using the Parlett recurrence algorithm. It is also proposed to perform some scalar operations (such as the building of interpolating polynomials) with an enlarged number of significant decimal digits.

The interactions between spin of fermionic matter and torsion in Einstein-Cartan-Sciama-Kibble (ECSK) theory of gravity provide a repulsive gravitational potential at very dense states of fermionic matter, which prevents the formation of black hole singularities inside the deeper horizon. While the fermionic matter in the black hole is attracted by the black hole at the beginning, after a critical point it is repelled to bounce at a critical high density and then expand into other side of the horizon as a newly created space, which may be considered as a non-singular, closed universe. We constructed the action of these fermions in a black hole with torsion in the framework of ECSK theory of gravity from which the free Dirac action is inferred and the interaction potential is obtained. Also, this scenario naturally solves the flatness and horizon problems of cosmology without introducing finely tuned scalar fields, or more complicated functions of the Ricci scalar R in gravitational action.

We investigate the time evolution of odd entanglement entropy (OEE) and logarithmic negativity (LN) for the thermofield double (TFD) states in free scalar quantum field theories using the covariance matrix approach. To have mixed states, we choose non-complementary subsystems, either adjacent or disjoint intervals on each side of the TFD. We find that the time evolution pattern of OEE is a linear growth followed by saturation. On a circular lattice, for longer times the finite size effect demonstrates itself as oscillatory behavior. In the limit of vanishing mass, for a subsystem containing a single degree of freedom on each side of the TFD, we analytically find the effect of zero-mode on the time evolution of OEE which leads to logarithmic growth in the intermediate times. Moreover, for adjacent intervals we find that the LN is zero for times $t < \beta/2$ (half of the inverse temperature) and after that, it begins to grow linearly. For disjoint intervals at fixed temperature, the vanishing of LN is observed for times $t, Comment: 44 pages, 17 figures, Comments about memory effect and some references are added

We consider 5-point functions in conformal field theories in d > 2 dimensions. Using weight-shifting operators, we derive recursion relations which allow for the computation of arbitrary conformal blocks appearing in 5-point functions of scalar operators, reducing them to a linear combination of blocks with scalars exchanged. We additionally derive recursion relations for the conformal blocks which appear when one of the external operators in the 5-point function has spin 1 or 2. Our results allow us to formulate positivity constraints using 5-point functions which describe the expectation value of the energy operator in bilocal states created by two scalars., 104 pages, 1 attached Mathematica notebook; V2: small adjustments, references added; V3: clarifications and some formulas corrected

Our understanding of quantum correlators in cosmological spacetimes, including those that we can observe in cosmological surveys, has improved qualitatively in the past few years. Now we know many constraints that these objects must satisfy as consequences of general physical principles, such as symmetries, unitarity and locality. Using this new understanding, we derive the most general scalar four-point correlator, i.e., the trispectrum, to all orders in derivatives for manifestly local contact interactions. To obtain this result we use techniques from commutative algebra to write down all possible scalar four-particle amplitudes without assuming invariance under Lorentz boosts. We then input these amplitudes into a contact reconstruction formula that generates a contact cosmological correlator in de Sitter spacetime from a contact scalar or graviton amplitude. We also show how the same procedure can be used to derive higher-point contact cosmological correlators. Our results further extend the reach of the boostless cosmological bootstrap and build a new connection between flat and curved spacetime physics., 31 pages

The aim of this investigation is to examine the effect of gravitational modification, in particular, the f ( G , T ) gravitational field, for dynamically relativistic spherically symmetric systems in the existence of electromagnetic field. The theoretical analysis of dynamical variables linked with charged viscous anisotropic sphere with dissipation is formulated in these environments. We consider that with a relativistic matter, the non-static diagonally symmetric spherical structure is coupled. We linked the Weyl scalar, structure parameters including the charged terms with metric scale factors and mass function. To formulate general form of dynamical variables, we implemented Herrera’s methodology for the orthogonally decomposition of the Riemann tensor. The presence of these variables in the behavioral dynamics of radiating spheres is then analyzed. With the existence and exclusion of fixed f ( G , T ) values, the parameters essential for the occurrence of inhomogeneities have been studied. It is suggested that with generalized forms of scalar variables, the evolutionary periods of the spherical interiors can be well observed.