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The basis digraphs of p-schemesSep 29 2007It is proved that association schemes with bipartite basis graphs are exactly 2-schemes. This result follows from a characterization of p-schemes for an arbitrary prime p in terms of basis digraphs.

The Application of Tridiagonal Matrices in P-polynomial Table AlgebrasJun 14 2019In this paper, we study the characters of two classes of P-polynomial table algebras using tridiagonal matrices. To this end, we obtain some results about the eigen-structure of special tridiagonal matrices. We also find a recursive relation for the characteristic ... More

On circular-arc graphs with association schemesJan 26 2015In this paper, we give a characterization of the class of all circular-arc graphs whose schemes are association. Moreover, all association schemes which are the scheme of a circular-arc graph are characterized, specially it is proved that they are Schurian. ... More

On Characters of a Class of P-polynomial table algebras and applicationsJul 10 2019In this paper, we study the characters of homogeneous monotonic P-polynomial table algebras with finite dimension d>=5. We then apply them to association schemes. To this end, we develop some methods using tridiagonal matrices and Z-transform. Moreover, ... More

Burnside-Brauer Theorem and Character Products in Table AlgebrasOct 29 2008Apr 14 2009In this paper, we first show that the irreducible characters of a quotient table algebra modulo a normal closed subset can be viewed as the irreducible characters of the table algebra itself. Furthermore, we define the character products for table algebras ... More

Standard Character Condition for C-algebrasMar 17 2008It is well known that the adjacency algebra of an association scheme has the standard character. In this paper we first define the concept of standard character for C-algebras and we say that a C-algebra has the {\it standard character condition} if it ... More

On amorphic C-algebrasNov 05 2005Jan 02 2006An amorphic association scheme has the property that any of its fusion is also an association scheme. In this paper we generalize the property to be amorphic to an arbitrary C-algebra and prove that any amorphic C-algebra is determined up to isomorphism ... More

On cyclotomic schemes over finite near-fieldsNov 16 2006We introduce a concept of cyclotomic association scheme C over a finite near-field. It is proved that if C is nontrivial, then Aut(C)<AGL(V) where V is the linear space associated with the near-field. In many cases we are able to get more specific information ... More

Optimal weighted Hardy-Rellich inequalities on $H^2\cap H^{1}_{0}$Oct 07 2009We give necessary and sufficient conditions on a pair of positive radial functions $V$ and $W$ on a ball $B$ of radius $R$ in $R^{n}$, $n \geq 1$, so that the following inequalities hold \begin{equation*} \label{two} \hbox{$\int_{B}V(x)|\nabla u |^{2}dx ... More

Correlation of Scholarly Networks and Social NetworksNov 19 2014In previous studies, much attention from multidisciplinary fields has been devoted to understand the mechanism of underlying scholarly networks including bibliographic networks, citation networks and co-citation networks. Particularly focusing on networks ... More

Invariants of some compactified Picard modular surfaces and applicationsNov 12 2014The paper investigates invariants of compactified Picard modular surfaces by principal congruence subgroups of Picard modular groups. The applications to the surface classification and modular forms are discussed.

Notes on a scalar field with a kinetic term non-minimally coupled to gravityFeb 27 2014Sep 15 2014We explore the inflationary phase of a scalar field with a kinetic term non-minimally coupled to gravity. We find that one of the slow-roll conditions is naturally consequence of the equation of motion of the scalar field. Thus, slow-roll conditions impose ... More

A new phase of scalar field with a kinetic term non-minimally coupled to gravityMar 03 2013Jul 27 2013We consider the dynamics of a scalar field non-minimally coupled to gravity in the context of cosmology. It is demonstrated that there exists a new phase for the scalar field, in addition to the inflationary and dust-like (reheating period) phases. Analytic ... More

On the Relation between Centrality Measures and Consensus AlgorithmsAug 08 2012This paper introduces some tools from graph theory and distributed consensus algorithms to construct an optimal, yet robust, hierarchical information sharing structure for large-scale decision making and control problems. The proposed method is motivated ... More

Affine embeddings of Cantor sets on the lineJul 11 2016Aug 09 2016Let $s\in (0,1)$, and let $F\subset \mathbb{R}$ be a self similar set such that $0 < \dim_H F \leq s$ . We prove that there exists $\delta= \delta(s) >0$ such that if $F$ admits an affine embedding into a homogeneous self similar set $E$ and $0 \leq \dim_H ... More

Efficient Cosmological Parameter Estimation with Hamiltonian Monte CarloAug 30 2006Aug 31 2006Traditional Markov Chain Monte Carlo methods suffer from low acceptance rate, slow mixing and low efficiency in high dimensions. Hamiltonian Monte Carlo resolves this issue by avoiding the random walk. Hamiltonian Monte Carlo (HMC) is a Markov chain Monte ... More

Dimensional Analysis and electric potential due to a uniformly charged sheetMar 10 2011Dimensional analysis, superposition principle, and continuity of electric potential are used to study electric potential of a uniformly charged square sheet at its plane. It is shown that knowing the electric potential on the diagonal and inside the square ... More

New Tests of Uniformity on the Compact Classical Groups as Diagnostics for Weak-star Mixing of Markov ChainsDec 10 2016Feb 25 2018This paper introduces two new families of non-parametric tests of goodness-of-fit on the compact classical groups. One of them is a family of tests for the eigenvalue distribution induced by the uniform distribution, which is consistent against all fixed ... More

Left $φ$-biprojectivity of some Banach algebrasMay 14 2019In this paper, we introduce a homological notion of left $\phi$-biprojectivity for Banach algebras, where $\phi$ is a non-zero multiplicative linear functional. We show that for a locally compact group $G$, the Segal algebra $S(G)$ is left $\phi$-contractible ... More

A Predictive Model for Notional Anaphora in EnglishApr 19 2018Notional anaphors are pronouns which disagree with their antecedents' grammatical categories for notional reasons, such as plural to singular agreement in: 'the government ... they'. Since such cases are rare and conflict with evidence from strictly agreeing ... More

On the associated primes of generalized local cohomology modulesOct 13 2005Let $\fa$ be an ideal of a commutative Noetherian ring $R$ with identity and let $M$ and $N$ be two finitely generated $R$-modules. Let $t$ be a positive integer. It is shown that $\Ass_R(H_{\fa}^t(M,N))$ is contained in the union of the sets $\Ass_R(\Ext_R^i(M,H_{\fa}^{t-i}(N)))$, ... More

Approximate biflatness and Johnson pseudo-contractibility of some Banach algebrasJun 11 2018Aug 30 2018In this paper, we study the structure of Lipschitz algebras under the notions of approximate biflatness and Johnson pseudo-contractibility. We show that for a compact metric space $X,$ the Lipschitz algebras $Lip_{\alpha}(X)$ and $\ell ip_{\alpha}(X)$ ... More

Fake quadrics from irreducible lattices acting on the product of upper half planesMay 22 2013In the present article, we provide examples of fake quadrics, that is, minimal complex surfaces of general type with the same numerical invariants as the smooth quadric in $\PP ^3$ which are quotients of the bidisc by an irreducible lattice of automorphisms. ... More

Cauchy Identities for the Characters of the Compact Classical GroupsOct 14 2016Motivated by statistical applications, this paper introduces Cauchy identities for characters of the compact classical groups. These identities generalize the well-known Cauchy identity for characters of the unitary group, which are Schur functions of ... More

The Wasserstein Distances Between Pushed-Forward Measures with Applications to Uncertainty QuantificationFeb 14 2019In the study of dynamical and physical systems, the input parameters are often uncertain or randomly distributed according to a measure $\varrho$. The system's response $f$ pushes forward $\varrho$ to a new measure $f\circ \varrho$ which we would like ... More

On the computation of the Ratliff-Rush closure, associated graded ring and invariance of a lengthNov 02 2015Let $(R,\fm)$ be a Cohen-Macaulay local ring of positive dimension $d$ and infinite residue field. Let $I$ be an $\fm$-primary ideal of $R$ and $J$ be a minimal reduction of $I$. In this paper we show that if $\widetilde{I^k}=I^k$ and $J\cap I^n=JI^{n-1}$ ... More

Avoiding Undesired Choices Using Intelligent Adaptive SystemsApr 10 2014We propose a number of heuristics that can be used for identifying when intransitive choice behaviour is likely to occur in choice situations. We also suggest two methods for avoiding undesired choice behaviour, namely transparent communication and adaptive ... More

Gamma-Ray bursts: Energetics and Prompt CorrelationsAug 05 2013A model is presented here that is capable of simultaneously describing the luminosity function and the underlying joint population distribution of the prompt spectral and temporal parameters of Gamma-Ray Bursts (GRBs), subject to the detection threshold ... More

Implications of the primordial anisotropy for a scalar field with non-minimal kinetic couplingJul 21 2014We consider a scalar field with a kinetic term non-minimally coupled to gravity in an anisotropic background. Various potentials for the scalar field are considered. By explicit examples, we show that how the anisotropy can change the dynamics of the ... More

Ratliff-Rush ideal and reduction numbersOct 08 2015Let $(R,\fm)$ be a Cohen-Macaulay local ring of positive dimension $d$ and infinite residue field. Let $I$ be an $\fm$-primary ideal and $J$ a minimal reduction of $I$. In this paper, we show that $\widetilde{r_J(I)}\leq r_J(I)$. This answer to a question ... More

A new perspective on Gauge-flationJun 08 2012Sep 29 2012Recently Maleknejad and Sheikh-Jabbari have proposed a new model for inflation with non-Abelian gauge fields (Gauge-flation), and they have studied the model by numerical methods\cite{Sheikh}. In this model, the isotropy of space-time is recovered by ... More

Sharpness of Zapolsky inequality for quasi-states and Poisson bracketsJan 08 2011Zapolsky inequality gives a lower bound for the L1 norm of the Poisson bracket of a pair of C1 functions on the two-dimensional sphere by means of quasi-states. Here we show that this lower bound is sharp.

Algebraic properties of product of graphsJan 03 2011Jan 07 2011Let $G$ and $H$ be two simple graphs and let $G*H$ denotes the graph theoretical product of $G$ by $H$. In this paper we provide some results on graded Betti numbers, Castelnuovo-Mumford regularity, projective dimension, $h$-vector, and Hilbert series ... More

Angle constrained path to cluster multiple manifoldsFeb 21 2018In this paper, we propose a method to cluster multiple intersected manifolds. The algorithm chooses several landmark nodes randomly and then checks whether there is an angle constrained path between each landmark node and every other node in the neighborhood ... More

On the Impulsive Formation Control of Spacecraft Under Path ConstraintsNov 20 2018Feb 24 2019This paper deals with the impulsive formation control of spacecraft in the presence of constraints on the position vector and time. Determining a set of path constraints can increase the safety and reliability in an impulsive relative motion of spacecraft. ... More

Multiple Manifold Clustering Using Curvature Constrained PathDec 04 2018The problem of multiple surface clustering is a challenging task, particularly when the surfaces intersect. Available methods such as Isomap fail to capture the true shape of the surface nearby the intersection and result in incorrect clustering. The ... More

Modeling and Experimental Verification of Adaptive 100% Stator Ground Fault Protection Schemes for Synchronous GeneratorsApr 21 2018Salient pole synchronous generators as the main component of an electricity generation station should be carefully maintained and their operation has to be monitored such that any damage on them is avoided. Otherwise, the generating station might experience ... More

Detecting Kissing Scenes in a Database of Hollywood FilmsJun 05 2019Detecting scene types in a movie can be very useful for application such as video editing, ratings assignment, and personalization. We propose a system for detecting kissing scenes in a movie. This system consists of two components. The first component ... More

Magnetic Fields in Accretion Disks: A ReviewApr 21 2019Apr 23 2019We review the current theoretical models of the inward advection of the large scale external magnetic fields in accretion discs. The most plausible theories for launching astrophysical jets rely on strong magnetic fields at the inner parts of the host ... More

Sylvester-Gallai type theorems for quadratic polynomialsApr 12 2019We prove Sylvester-Gallai type theorems for quadratic polynomials. Specifically, we prove that if a finite collection $\mathcal Q$, of irreducible polynomials of degree at most $2$, satisfy that for every two polynomials $Q_1,Q_2\in {\mathcal Q}$ there ... More

Existence and structure of minimizers of least gradient problemsDec 26 2016We study existence of minimizers of the general least gradient problem \[\inf_{u \in BV_f} \int_{\Omega}\varphi(x,Du),\] where $BV_f=\{u \in BV(\Omega): \ \ u|_{\partial \Omega}=f\}$, $f\in L^{1}(\partial \Omega)$, and $\varphi(x,\xi)$ is convex, continuous, ... More

Measures Invariant Under Horospherical Subgroups in Positive characteristicOct 26 2010We prove measure rigidity for the action of (maximal) horospherical subgroups on homogeneous spaces obtained by quotient by a uniform (nonuniform) arithmetic lattices over a field of positive characteristic.

A simultaneous version of Host's equidistribution TheoremApr 29 2019Let $\mu$ be a probability measure on $\mathbb{R}/\mathbb{Z}$ that is ergodic under the $\times p$ map, with positive entropy. In 1995, Host showed that if $\gcd(m,p)=1$ then $\mu$ almost every point is normal in base $m$. In 2001, Lindenstrauss showed ... More

Analysis of the apparent lack of power in the cosmic microwave background anisotropy at large angular scalesFeb 27 2007We study the apparent lack of power on large angular scales in the WMAP data. We confirm that although there is no apparent lack of power at large angular scales for the full-sky maps, the lowest multipoles of the WMAP data happen to have the magnitudes ... More

Super-hot (T > 30 MK) Thermal Plasma in Solar FlaresMay 10 2011May 12 2011The Sun offers a convenient nearby laboratory to study the physical processes of particle acceleration and impulsive energy release in magnetized plasmas that occur throughout the universe, from planetary magnetospheres to black hole accretion disks. ... More

On the critical dimension of a fourth order elliptic problem with negative exponentMay 12 2009We study the regularity of the extremal solution of the semilinear biharmonic equation $\beta \Delta^2 u-\tau \Delta u=\frac{\lambda}{(1-u)^2}$ on a ball $B \subset \R^N$, under Navier boundary conditions $u=\Delta u=0$ on $\partial B$, where $\lambda ... More

Emerging Computing Technologies in High Energy PhysicsOct 19 2009While in the early 90s High Energy Physics (HEP) lead the computing industry by establishing the HTTP protocol and the first web-servers, the long time-scale for planning and building modern HEP experiments has resulted in a generally slow adoption of ... More

A note on approximately biflat banach algebrasJun 27 2016In this paper, we study the notion of approximately bi at Banach algebras for second dual Banach algebras and semigroup algebras. We show that for a locally compact group G, if S(G)?? is approximately bi at, then G is amenable group. Also we give some ... More

Notes on diffeomorphisms symmetry of $f(R)$ gravity in the cosmological contextOct 19 2015Feb 29 2016We study the metric perturbations in the context of restricted $f(R)$ gravity, in which a parameter for deviation from the full diffeomorphisms of space-time is introduced. We demonstrate that one can choose the parameter to remove the induced anisotropic ... More

An elementary exposition to topological overlap in the planeAug 04 2015The aim of this text is to provide an elementary and self-contained exposition of Gromov's argument on topological overlap (the presentation is based on Gromov's work, as well as two follow-up papers of Matousek and Wagner, and of Dotterrer, Kaufman and ... More

Curiosity about the dust matter in the cosmological contextSep 20 2013Oct 20 2013We propose a model for the dust matter in the cosmological context. The model contains a scalar field with a kinetic term nonminimally coupled to gravity. By investigating the background and perturbative equations, it is demonstrated that the scalar field ... More

The point of departure of a particle sliding on a curved surfaceJun 15 2012A particle is thrown tangentially on a surface. It is shown that for some surfaces and for special initial velocities the thrown particle leaves immediately the surface, and for special conditions it never leaves the surface. The conditions for leaving ... More

On the existence of J-class operatorsSep 17 2010In this note we answer in the negative the question raised by G.Costakis and A.Manoussos, whether there exists a J-class operator on every non-separable Banach space. In par- ticular we show that there exists a non-separable Banach space constructed by ... More

Some properties of generalized local cohomology modulesNov 06 2005Let $R$ be a commutative Noetherian ring, $\fa$ an ideal of $R$, $M$ and $N$ be two finitely generated $R$-modules. Let $t$ be a positive integer. We prove that if $R$ is local with maximal ideal $\fm$ and $ M\otimes_R N$ is of finite length then $H_{\fm}^t(M,N)$ ... More

Least Gradient Problems with Neumann Boundary ConditionDec 26 2016Mar 06 2017We study existence of minimizers of the least gradient problem \[\inf_{v \in BV_g} \int_{\Omega}\varphi(x, Dv),\] where $BV_g=\{v \in BV(\Omega): \int_{\partial \Omega}gv=1\}$, $\varphi(x,p): \Omega\times \R^n \rightarrow \R$ is a convex, continuous, ... More

On Traces of Singular ModuliMay 27 2019Jun 04 2019These notes are a detailed introduction to the first half of the article \textit{Traces of Singular Moduli} by Don Zagier.

Detuning control of Rabi vortex oscillations in light matter couplingJan 29 2019Jun 06 2019We study analytically the dynamics of vortices in strongly coupled exciton--photon fields in the presence of energy detuning. We derive equations for the vortex core velocity and mass, where they mainly depend on Rabi coupling and the relative distance ... More

A Dual Approach To The Advanced Calculus Via Lebesgue's IntegralDec 24 2009Apr 27 2014The paper suggests a slightly more rigorous justification to Wang et al.'s work from 2007, and introduces the Slanted Line Integral.

On (approximate) homological notions of certain Banach algebrasJun 05 2018In this paper, we study the notion of $\phi$-biflatness, $\phi$-biprojectivity, approximate biprojectivity and Johnson pseudo-contractibility for a new class of Banach algebras. Using this class of Banach algebras we give some examples which are approximately ... More

On the computation of the Ratliff-Rush closure, associated graded ring and invariance of a lengthNov 02 2015May 31 2017Let $(R,\fm)$ be a Cohen-Macaulay local ring of positive dimension $d$ and infinite residue field. Let $I$ be an $\fm$-primary ideal of $R$ and $J$ be a minimal reduction of $I$. In this paper we show that if $\widetilde{I^k}=I^k$ and $J\cap I^n=JI^{n-1}$ ... More

On left $φ$-biprojectivity and left $φ$-biflatness of certain Banach algebrasMay 14 2019In this paper, we study left $\phi$-biflatness and left $\phi$-biprojectivity of some Banach algebras, where $\phi$ is a non-zero multiplicative linear function. We show that if the Banach algebra $A^{**}$ is left $\phi$-biprojective, then $A$ is left ... More

Arithmetic of a fake projective plane and related elliptic surfacesMar 05 2008Nov 21 2008The purpose of the present paper is to explain the fake projective plane constructed by J.H. Keum from the point of view of arithmetic ball quotients. Beside the ball quotient associated with the fake projective plane, we also analize two further naturally ... More

Can Eye Movement Data Be Used As Ground Truth For Word Embeddings Evaluation?Apr 23 2018In recent years a certain success in the task of modeling lexical semantics was obtained with distributional semantic models. Nevertheless, the scientific community is still unaware what is the most reliable evaluation method for these models. Some researchers ... More

New constructions of WOM codes using the Wozencraft ensembleOct 30 2011In this paper we give several new constructions of WOM codes. The novelty in our constructions is the use of the so called Wozencraft ensemble of linear codes. Specifically, we obtain the following results. We give an explicit construction of a two-write ... More

The 2-Parametric Extension of $h$ Deformation of $GL(2)$, and The Differential Calculus on Its Quantum PlaneJun 16 1993We present an alternative 2-parametric deformation $ GL(2)_{h,h'} $ , and construct the differential calculus on the quantum plane on which this quantum group acts. Also we give a new deformation of the two dimensional Heisenberg algebra

Capacity achieving multiwrite WOM codesSep 05 2012In this paper we give an explicit construction of a capacity achieving family of binary t-write WOM codes for any number of writes t, that have a polynomial time encoding and decoding algorithms. The block length of our construction is N=(t/\epsilon)^{O(t/(\delta\epsilon))} ... More

Distributed Multi-objective Multidisciplinary Design Optimization AlgorithmsAug 12 2012Sep 16 2012This work proposes multi-agent systems setting for concurrent engineering system design optimization and gradually paves the way towards examining graph theoretic constructs in the context of multidisciplinary design optimization problem. The flow of ... More

Observational signatures of sub-photospheric radiation mediated shocks in the prompt phase of GRBsMay 15 2012Jun 27 2012A shock that form below the photosphere of a GRB outflow is mediated by Compton scattering of radiation advected into the shock by the upstream fluid. The characteristic scale of such a shock, a few Thomson depths, is larger than any kinetic scale involved ... More

Generalized notion of amenability for a class of matrix algebrasJun 27 2016We investigate the notions of amenability and its related homological notions for a class of I ?I-upper triangular matrix algebra, say UP(I;A), where A is a Banach algebra equipped with a non- zero character. We show that UP(I;A) is pseudo-contractible ... More

Varieties of general type with the same Betti numbers as $\mathbb P^1\times \mathbb P^1\times\ldots\times \mathbb P^1$Nov 12 2014We study quotients $\Gamma\backslash \mathbb H^n$ of the $n$-fold product of the upper half plane $\mathbb H$ by irreducible and torsion-free lattices $\Gamma < PSL_2(\mathbb R)^n$ with the same Betti numbers as the $n$-fold product $(\mathbb P^1)^n$ ... More

Effect of strain path on deformation texture of superconducting niobium sheetMar 30 2014The texture of high purity superconducting niobium sheets plays an important role in the physical and mechanical properties of high purity niobium sheet that are important for manufacturing of superconducting accelerator cavities. In a particular batch ... More

A Multivariate Fit Luminosity Function and World Model for Long GRBsSep 20 2012Jan 21 2013It is proposed that the luminosity function, the rest-frame spectral correlations and distributions of cosmological Long-duration (Type-II) Gamma-Ray Bursts (LGRBs) may be very well described as multivariate log-normal distribution. This result is based ... More

Universal frequency-dependent conduction of electron glassesMar 12 2014Mar 31 2014Characterizing the frequency-dependent response of amorphous systems and glasses can provide important insights into their physics. Here, we study the response of an electron glass, where Coulomb interactions are important and have previously been shown ... More

0^# and elementary end extensions of V_kMay 17 2000In this paper we prove that if k is a cardinal in L[0^#], then there is an inner model M such that M |= (V_k,E) has no elementary end extension. In particular if 0^# exists then weak compactness is never downwards absolute. We complement the result with ... More

Cauchy Identities for the Characters of the Compact Classical GroupsOct 14 2016Nov 17 2016Motivated by statistical applications, this paper introduces Cauchy identities for characters of the compact classical groups. These identities generalize the well-known Cauchy identity for characters of the unitary group, which are Schur functions of ... More

The Bayesian SLOPEAug 31 2016Sep 01 2016The SLOPE estimates regression coefficients by minimizing a regularized residual sum of squares using a sorted-$\ell_1$-norm penalty. The SLOPE combines testing and estimation in regression problems. It exhibits suitable variable selection and prediction ... More

Detuning control of vortex oscillations in light matter couplingJan 29 2019We study analytically the dynamics of vortices in strong--coupled exciton--photon fields in the presence of energy detuning. We derive equations for the vortex core velocity and mass, where they mainly depend on Rabi coupling and the relative distance ... More

Measurement of the energy dependence of the photon-proton total cross section with the ZEUS detector at HERADec 28 2010The energy dependence of the photon-proton total cross section was determined from positron-proton scattering data collected with the ZEUS detector at HERA at three values of the center-of-mass energy, W, of the \gamma p system in the range 194<W<296 ... More

Some results on local cohomology modulesDec 03 2005Let $R$ be a commutative Noetherian ring, $\fa$ an ideal of $R$, and let $M$ be a finitely generated $R$-module. For a non-negative integer $t$, we prove that $H_{\fa}^t(M)$ is $\fa$-cofinite whenever $H_{\fa}^t(M)$ is Artinian and $H_{\fa}^i(M)$ is $\fa$-cofinite ... More

Strategy-Proof Incentives for PredictionsMay 13 2018Dec 04 2018Our aim is to design mechanisms that motivate all agents to reveal their predictions truthfully and promptly. For myopic agents, proper scoring rules induce truthfulness. However, when agents have multiple opportunities for revealing information, and ... More

A Novel Pixel-Averaging Technique for Extracting Training Data from a Single Image, Used in ML-Based Image EnlargementMar 25 2019Size of the training dataset is an important factor in the performance of a machine learning algorithms and tools used in medical image processing are not exceptions. Machine learning tools normally require a decent amount of training data before they ... More

Robin Spectral Rigidity of the EllipseDec 23 2018In this paper, we investigate $C^1$ isospectral deformations of the ellipse with Robin boundary conditions, allowing both the Robin function and domain to deform simultaneously. We prove that if the deformations preserve the reflectional symmetries of ... More

Parallel Matrix-Free Implementation of Frequency-Domain Finite Difference Methods for Cluster ComputingMay 23 2017Full-wave 3D electromagnetic simulations of complex planar devices, multilayer interconnects, and chip packages are presented for wide-band frequency-domain analysis using the finite difference integration technique developed in the PETSc software package. ... More

The Wasserstein Distances Between Pushed-Forward Measures with Applications to Uncertainty QuantificationFeb 14 2019Feb 20 2019In the study of dynamical and physical systems, the input parameters are often uncertain or randomly distributed according to a measure $\varrho$. The system's response $f$ pushes forward $\varrho$ to a new measure $f\circ \varrho$ which we would like ... More

Unipotent Flows And Isotropic Quadratic Forms In Positive CharacteristicOct 26 2010The analogous statement to Oppenheim conjecture over a local field of positive characteristic is proved. The dynamical argument is most involved in the case of characteristic 3.

A special case of effective equidistribution with explicit constantsOct 26 2010An effective equidistribution with explicit constants for the isometry group of rational forms with signature $(2,1)$ is proved. As an application we get an effective discreteness of Markov spectrum.

A Survey of Word Embeddings Evaluation MethodsJan 21 2018Word embeddings are real-valued word representations able to capture lexical semantics and trained on natural language corpora. Models proposing these representations have gained popularity in the recent years, but the issue of the most adequate evaluation ... More

The singular extremal solutions of the bilaplacian with exponential nonlinearityMay 12 2009Consider the problem {ll} \Delta^2 u= \lambda e^{u} &\text{in} B u=\frac{\partial u}{\partial n}=0 &\text{on}\partial B, where $B$ is the unit ball in $\R^N$ and $\lambda$ is a parameter. Unlike the Gelfand problem the natural candidate $u=-4\ln(|x|)$, ... More

A geometrical relation between symmetric operators and mutually unbiased operatorsMay 26 2013In this work we study the relation between the set of symmetric operators and the set of mutually unbiased operators from finite plane geometry point of view. Here symmetric operators are generalization of symmetric informationally complete probability-operator ... More

Lower bounds for covolumes of arithmetic lattices in $PSL_2(\mathbb R)^n$Jan 26 2015We study the covolumes of arithmetic lattices in $PSL_2(\mathbb R)^n$ for $n\geq 2$ and identify uniform and non-uniform irreducible lattices of minimal covolume. More precisely, let $\mu$ be the Euler-Poincar\'e measure on $PSL_2(\mathbb R)^n$ and $\chi=\mu/2^n$. ... More

On approximately left phi-biprojective Banach algebrasJun 27 2016Aug 26 2016In this paper, for a Banach algebra A, we introduced the new notions of approximately left $\phi$-biprojective and approximately left character biprojective, where $\phi$ is a non-zero multiplicative linear functional on A. We show that for SIN group ... More

Lower Bounds for Matrix ProductJan 02 2002We prove lower bounds on the number of product gates in bilinear and quadratic circuits that compute the product of two $n \cross n$ matrices over finite fields. In particular we obtain the following results: 1. We show that the number of product gates ... More

Are There Echoes From The Pre-Big Bang Universe? A Search for Low Variance Circles in the CMB SkyDec 08 2010The existence of concentric low variance circles in the CMB sky, generated by black-hole encounters in an aeon preceding our big bang, is a prediction of the Conformal Cyclic Cosmology. Detection of three families of such circles in WMAP data was recently ... More

Algebraic cycles and motivic iterated integrals IIJun 30 2008This is a sequel to our previous paper (joint with Furusho). It will give a more natural framework for constructing elements in the Hopf algebra of framed mixed Tate motives according to Bloch and Kriz. This framework allows us to extend our previous ... More

Cell size regulation in microorganismsDec 23 2013Apr 08 2014Various rod-shaped bacteria such as the canonical gram negative Escherichia coli or the well-studied gram positive Bacillus subtilis divide symmetrically after they approximately double their volume. Their size at division is not constant, but is typically ... More

Magnetic fields in accretion disks: a reviewApr 21 2019We review the current theoretical models of the inward advection of the large scale external magnetic fields in accretion discs. The most plausible theories for launching astrophysical jets rely on strong magnetic fields at the inner parts of the host ... More

Stress-constrained continuum topology optimization: a new approach based on elasto-plasticityAug 23 2016A new approach for generating stress-constrained topological designs in continua is presented. The main novelty is in the use of elasto-plastic modeling and in optimizing the design such that it will exhibit a linear-elastic response. This is achieved ... More

Interpolation Theorems for Nonmonotonic Reasoning SystemsJul 16 2002Craig's interpolation theorem (Craig 1957) is an important theorem known for propositional logic and first-order logic. It says that if a logical formula $\beta$ logically follows from a formula $\alpha$, then there is a formula $\gamma$, including only ... More

Kinematic & Dynamic Analysis of the Human Upper Limb Using the Theory of ScrewsJun 06 2019Screw theory provides geometrical insight into the mechanics of rigid bodies. Screw axis is defined as the line coinciding with the joint axis. Line transformations in the form of a screw operator are used to determine the joint axes of a seven degree ... More

Compositional pre-training for neural semantic parsingMay 27 2019Semantic parsing is the process of translating natural language utterances into logical forms, which has many important applications such as question answering and instruction following. Sequence-to-sequence models have been very successful across many ... More