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Poincare series of some pure and mixed trace algebras of two generic matricesSep 09 2006We work over a field K of characteristic zero. The Poincare series for the algebra C_{n,2} of GL_n-invariants and the algebra T_{n,2} of GL_n-concomitants of two generic n x n matrices x and y are presented for n less than or equal 6. Both simply graded ... More

Small orders of Hadamard matrices and base sequencesAug 12 2010We update the list of odd integers n<10000 for which an Hadamard matrix of order 4n is known to exist. We also exhibit the first example of base sequences BS(40,39). Consequently, there exist T-sequences TS(n) of length n=79. The first undecided case ... More

Classification of normal sequencesAug 03 2010Base sequences BS(m,n) are quadruples (A;B;C;D) of {+1,-1}-sequences, with A and B of length m and C and D of length n, such that the sum of their nonperiodic autocorrelation functions is a delta-function. Normal sequences NS(n) are base sequences (A;B;C;D) ... More

Hadamard matrices from base sequences: An exampleFeb 21 2010There are several well-known methods that one can use to construct Hadamard matrices from base sequences BS(m,n). In view of the recent classification of base sequences BS(n+1,n) for n <= 30, it may be of interest to show on an example how prolific these ... More

Skew-Hadamard matrices of orders 436, 580 and 988 existJun 13 2007We construct two difference families on each of the cyclic groups of order 109, 145 and 247, and use them to construct skew-Hadamard matrices of orders 436, 580 and 988. Such difference families and matrices are constructed here for the first time. The ... More

Skew-Hadamard matrices of orders 188 and 388 existApr 04 2007Mar 26 2008We construct several difference families on cyclic groups of orders 47 and 97, and use them to construct skew-Hadamard matrices of orders 188 and 388. Such difference families and matrices are constructed here for the first time. The matrices are constructed ... More

Generalization of Mirsky's theorem on diagonals and eigenvalues of matricesJun 17 2012Mirsky proved that, for the existence of a complex matrix with given eigenvalues and diagonal entries, the obvious necessary condition is also sufficient. We generalize this theorem to matrices over any field and provide a short proof. Moreover, we show ... More

Multigraded Poincare series for mixed states of two qubits and the boundary of the set of separable statesApr 26 2006May 08 2006Let M be the set of mixed states and S the set of separable states of the two-qubit system, and G = SU(2) x SU(2) the group of local unitary transformations (ignoring the overall phase factor). We compute the multigraded Poincare series for the algebra ... More

Symplectic polynomial invariants of one or two matrices of small sizeAug 23 2008Dec 23 2010The algebra of holomorphic polynomial Sp_{2n}-invariants of k complex 2n by 2n matrices (under diagonal conjugation action) is generated by the traces of words in these matrices and their symplectic adjoints. No concrete minimal generating set is known ... More

Generalized distillability conjecture and generalizations of Cauchy-Bunyakovsky-Schwarz inequality and Lagrange identityMay 24 2010Dec 22 2010Let rho_k, k=1,2,...,m, be the critical Werner state in a bipartite d_k by d_k quantum system, i.e., the one that separates the 1-distillable Werner states from those that are 1-indistillable. We propose a new conjecture (GDC) asserting that the tensor ... More

On orthostochastic, unistochastic and qustochastic matricesAug 30 2007We introduce qustochastic matrices as the bistochastic matrices arising from quaternionic unitary matrices by replacing each entry with the square of its norm. This is the quaternionic analogue of the unistochastic matrices studied by physicists. We also ... More

Normal Forms and Tensor Ranks of Pure States of Four QubitsDec 21 2006May 07 2007We examine the SLOCC classification of the (non-normalized) pure states of four qubits obtained by F. Verstraete et al. The rigorous proofs of their basic results are provided and necessary corrections implemented. We use Invariant Theory to solve the ... More

Normal forms for orthogonal similarity classes of skew-symmetric matricesMar 10 2006Dec 04 2006Let F be an algebraically closed field of characteristic different from 2. We show that every nonsingular skew-symmetric n by n matrix X over F is orthogonally similar to a bidiagonal skew-symmetric matrix. In the singular case one has to allow some 4-diagonal ... More

Goethals--Seidel difference families with symmetric or skew base blocksFeb 02 2018We single out a class of difference families which is widely used in some constructions of Hadamard matrices and which we call Goethals--Seidel (GS) difference families. They consist of four subsets (base blocks) of a finite abelian group of order $v$, ... More

Solution of the congruence problem for arbitrary hermitian and skew-hermitian matrices over polynomial ringsJun 10 2002We equip the complex polynomial algebra C[t] with the involution which is the identity on C and sends t to -t. Answering a question raised by V.G. Kac, we show that every hermitian or skew-hermitian matrix over this algebra is congruent to the direct ... More

An octonion algebra originating in combinatoricsFeb 14 2010Jun 16 2010C.H. Yang discovered a polynomial version of the classical Lagrange identity expressing the product of two sums of four squares as another sum of four squares. He used it to give short proofs of some important theorems on composition of delta-codes (now ... More

Verification of Atiyah's conjecture for some nonplanar configurations with dihedral symmetryAug 11 2002Aug 13 2002Atiyah's conjecture concerning configurations of N points in the Euclidean three-space is verified for the following nonplanar configurations: The first m points lie on a line L and the remaining n=N-m (>2) points are the vertices of a regular n-gon whose ... More

On two-distillable Werner statesMar 23 2010Jul 17 2016We consider bipartite mixed states in a $d\otimes d$ quantum system. We say that $\rho$ is PPT if its partial transpose $1 \otimes T (\rho)$ is positive semidefinite, and otherwise $\rho$ is NPT. The well-known Werner states are divided into three types: ... More

Hadamard matrices of small order and Yang conjectureDec 27 2009We show that 138 odd values of n less than 10000 for which one knows how to construct a Hadamard matrix of order 4n have been overlooked in the recent handbook of combinatorial designs. There are four additional odd n, namely 191, 5767, 7081 and 8249, ... More

Classification of near-normal sequencesMar 25 2009Sep 01 2009We introduce a canonical form for near-normal sequences NN(n), and using it we enumerate the equivalence classes of such sequences for even n up to 30. These sequences are needed for Yang multiplication in the construction of longer T-sequences from base ... More

Generalization of Scarpis's theorem on Hadamard matricesJan 04 2016A $\{1,-1\}$-matrix $H$ of order $m$ is a Hadamard matrix if $HH^T=mI_m$, where $T$ is the transposition operator and $I_m$ the identity matrix of order $m$. J. Hadamard published his paper on Hadamard matrices in 1893. Five years later, Scarpis showed ... More

The checkerboard family of entangled states of two qutritsNov 14 2009May 18 2010By modifying the method of Bruss and Peres, we construct two new families of entangled two qutrit states. For all density matrices in these families the (i,j)th entry is 0 for i+j odd. The first family depends on 27 independent real parameters and includes ... More

On the base sequence conjectureMar 07 2010Let BS(m,n) denote the set of base sequences (A;B;C;D), with A and B of length m and C and D of length n. The base sequence conjecture (BSC) asserts that BS(n+1,n) exist (i.e., are non-empty) for all n. This is known to be true for n <= 36 and when n ... More

Classification of base sequences BS(n+1,n)Feb 06 2010Apr 12 2010Base sequences BS(n+1,n) are quadruples of {1,-1}-sequences (A;B;C;D), with A and B of length n+1 and C and D of length n, such that the sum of their nonperiodic autocorrelation functions is a delta-function. The base sequence conjecture, asserting that ... More

Proof of Atiyah's conjecture for two special types of configurationsMay 21 2002Jun 11 2002We prove Atiyah's conjecture for two special types of configurations of N points in the three-dimensional Euclidean space. For one of these types, it is shown that the stronger conjecture of Atiyah and Sutcliffe is valid.

Periodic complementary sets of binary sequencesAug 01 2007Apr 13 2008Let PCS_p^N denote a set of p binary sequences of length N such that the sum of their periodic auto-correlation functions is a delta-function. In the 1990, Boemer and Antweiler addressed the problem of constructing such sequences. They presented a table ... More

Poincare series for local unitary invariants of mixed states of the qubit-qutrit systemMay 01 2006We consider the mixed states of the bipartite quantum system with the first party a qubit and the second a qutrit. The group of local unitary transformations of the system, ignoring the overall phase factor, is the direct product G of SU(2) and SU(3). ... More

Some new near-normal sequencesJul 17 2009Feb 14 2010The normal sequences NS(n) and near-normal sequences NN(n) play an important role in the construction of orthogonal designs and Hadamard matrices. They can be identified with certain base sequences (A;B;C;D), where A and B have length n+1 and C and D ... More

Supplementary difference sets with symmetry for Hadamard matricesMar 29 2009Dec 05 2009First we give an overview of the known supplementary difference sets (SDS) (A_i), i=1..4, with parameters (n;k_i;d), where k_i=|A_i| and each A_i is either symmetric or skew and k_1 + ... + k_4 = n + d. Five new Williamson matrices over the elementary ... More

Cyclic (v;r,s;lambda) difference families with two base blocks and v <= 50Jul 14 2007Mar 30 2009We construct many new cyclic (v;r,s;lambda) difference families with v less than or equal 50. In particular we construct the difference families with parameters (45;18,10;9), (45;22,22;21), (47;21,12;12), (47;19,15;12), (47;22,14;14), (48;20,10;10), (48;24,4;12), ... More

Hadamard matrices of order 764 existMar 11 2007We construct two Hadamard matrices of order 764. Both are of Goethals-Seidel type.

Dimensions of generic local orbits of multipartite quantum systemsAug 15 2006Jan 01 2007We consider the action of the group of local unitary transformations, U(m) x U(n), on the set of (mixed) states W of the bipartite m x n quantum system. We prove that the generic U(m) x U(n)--orbits in W have dimension m^2+n^2-2. This problem was mentioned ... More

A new Yang number and consequencesJul 30 2010Base sequences BS(m,n) are quadruples (A;B;C;D) of {+1,-1}-sequences, A and B of length m and C and D of length n, the sum of whose non-periodic auto-correlation functions is zero. Base sequences and some special subclasses of BS(n+1,n) known as normal ... More

On orthogonal and special orthogonal invariants of a single matrix of small orderSep 03 2007Mar 16 2008We study the structure of the algebra of polynomial invariants for the usual conjugation action of the complex special, SO_n, and general, O_n, orthogonal group on the space of traceless n by n complex matrices. (Note that these two algebras coincide ... More

Orthogonal product bases of four qubitsJun 20 2016An orthogonal product basis (OPB) of a finite-dimensional Hilbert space $H=H_1\otimes H_2\otimes\cdots\otimes H_n$ is an orthonormal basis of $H$ consisting of product vectors $x_1\otimes x_2\otimes\cdots\otimes x_n$. We show that the problem of classifying ... More

Proof of the Gour-Wallach conjectureAug 06 2013Aug 14 2013The absolute value of the hyperdeterminant of four qubits is a useful measure of genuine entanglement. We prove a recent conjecture of Gour and Wallach describing the pure maximally entangled four-qubit states with respect to this measure.

Properties and construction of extreme bipartite states having positive partial transposeMar 07 2012Jan 30 2013We consider a bipartite quantum system H_A x H_B with M=dim H_A and N=dim H_B. We study the set E of extreme points of the compact convex set of all states having positive partial transpose (PPT) and its subsets E_r={rho in E: rank rho=r}. Our main results ... More

Separability problem for multipartite states of rank at most fourJan 11 2013One of the most important problems in quantum information is the separability problem, which asks whether a given quantum state is separable. We investigate multipartite states of rank at most four which are PPT (i.e., all their partial transposes are ... More

Boundary of the set of separable statesApr 03 2014Sep 04 2015Motivated by the separability problem in quantum systems $2\otimes4$, $3\otimes3$ and $2\otimes2\otimes2$, we study the maximal (proper) faces of the convex body, $S_1$, of normalized separable states in an arbitrary quantum system with finite-dimensional ... More

Dimension formula for induced maximal faces of separable states and genuine entanglementJan 05 2015Jun 15 2015The normalized separable states of a finite-dimensional multipartite quantum system, represented by its Hilbert space ${\cal H}$, form a closed convex set ${\cal S}_1$. The set ${\cal S}_1$ has two kinds of faces, induced and non-induced. An induced face, ... More

On polynomial invariants of several qubitsApr 10 2008Feb 17 2009It is a recent observation that entanglement classification for qubits is closely related to local $SL(2,\CC)$-invariants including the invariance under qubit permutations, which has been termed $SL^*$ invariance. In order to single out the $SL^*$ invariants, ... More

Equivalence classes and canonical forms for two-qutrit entangled states of rank four having positive partial transposeMay 13 2012Sep 29 2012Let E' denote the set of non-normalized two-qutrit entangled states of rank four having positive partial transpose (PPT). We show that the set of SLOCC equivalence classes of states in E', equipped with the quotient topology, is homeomorphic to the quotient ... More

Description of rank four PPT entangled states of two qutritsMay 16 2011Nov 05 2011It is known that some two qutrit entangled states of rank 4 with positive partial transpose [PPT] can be built from the unextendible product bases [UPB]. We show that this fact is indeed universal, namely all such states can be constructed from UPB. We ... More

Qubit-qudit states with positive partial transposeSep 29 2012Dec 17 2012We show that the length of a qubit-qutrit separable state is equal to the max(r,s), where r is the rank of the state and s is the rank of its partial transpose. We refer to the ordered pair (r,s) as the birank of this state. We also construct examples ... More

The unextendible product bases of four qubits: Hasse diagramsSep 04 2018We consider the unextendible product bases (UPBs) of fixed cardinality $m$ in quantum systems of $n$ qubits. These UPBs are divided into finitely many equivalence classes with respect to an equivalence relation introduced by N. Johnston. There is a natural ... More

Nonexistence of $n$-qubit unextendible product bases of size $2^n-5$Sep 05 2017It is known that the $n$-qubit system has no unextendible product bases (UPBs) of cardinality $2^n-1$, $2^n-2$ and $2^n-3$. On the other hand the $n$-qubit UPBs of cardinality $2^n-4$ exist for all $n\ge3$. We prove that they do not exist for cardinality ... More

Universal subspaces for compact Lie groupsFeb 13 2008Dec 02 2009For a representation of a connected compact Lie group G in a finite dimensional real vector space U and a subspace V of U, invariant under a maximal torus of G, we obtain a sufficient condition for V to meet all G-orbits in U, which is also necessary ... More

Multiqubit UPB: The method of formally orthogonal matricesJan 26 2018Mar 01 2018We use formal matrices whose entries we view as vector variables taking unit vectors values in one-qubit Hilbert spaces of a multiqubit quantum system. We construct many unextendible product bases (UPBs) of new sizes in such systems and provide a new ... More

Non-positive-partial-transpose quantum states of rank four are distillableFeb 14 2016We show that any bipartite quantum state of rank four is distillable, when the partial transpose of the state has at least one negative eigenvalue, i.e., the state is NPT. For this purpose we prove that if the partial transpose of a two-qutrit NPT state ... More

Length filtration of the separable statesFeb 17 2016We investigate the separable states $\r$ of an arbitrary multipartite quantum system with Hilbert space $\cH$ of dimensionin $d$. The length $L(\r)$ of $\r$ is defined as the smallest number of pure product states having $\r$ as their mixture. The length ... More

Dimensions, lengths and separability in finite-dimensional quantum systemsJun 17 2012May 14 2013Many important sets of normalized states in a multipartite quantum system of finite dimension d, such as the set S of all separable states, are real semialgebraic sets. We compute dimensions of many such sets in several low-dimensional systems. By using ... More

Distillability and PPT entanglement of low-rank quantum statesJan 26 2011Jun 15 2011It is known that he bipartite quantum states, with rank strictly smaller than the maximum of the ranks of its two reduced states, are distillable by local operations and classical communication. Our first main result is that this is also true for NPT ... More

Zero patterns and unitary similarityJul 23 2008Dec 17 2009A subspace of the space, L(n), of traceless complex $n\times n$ matrices can be specified by requiring that the entries at some positions $(i,j)$ be zero. The set, $I$, of these positions is a (zero) pattern and the corresponding subspace of L(n) is denoted ... More

Orthogonal product bases of four qubitsJun 20 2016Jul 11 2017An orthogonal product basis (OPB) of a finite-dimensional Hilbert space $H=H_1\otimes H_2\otimes\cdots\otimes H_n$ is an orthonormal basis of $H$ consisting of product vectors $x_1\otimes x_2\otimes\cdots\otimes x_n$. We show that the problem of classifying ... More

Algorithms for difference families in finite abelian groupsJan 23 2018Apr 04 2018Our main objective is to show that the computational methods that we previously developed to search for difference families in cyclic groups can be fully extended to the more general case of arbitrary finite abelian groups. In particular the power density ... More

Quaternionic matrices: Unitary similarity, simultaneous triangularization and some trace identitiesSep 04 2007We construct six unitary trace invariants for 2 by 2 quaternionic matrices which separate the unitary similarity classes of such matrices, and show that this set is minimal. We prove two quaternionic versions of a well known characterization of triangularizable ... More

Some new periodic Golay pairsOct 22 2013Aug 27 2014Periodic Golay pairs are a generalization of ordinary Golay pairs. They can be used to construct Hadamard matrices. A positive integer $v$ is a (periodic) Golay number if there exists a (periodic) Golay pair of length $v$. Taking into the account the ... More

Compression of Periodic Complementary Sequences and ApplicationsFeb 04 2013A collection of complex sequences of length v is complementary if the sum of their periodic autocorrelation function values at all non-zero shifts is constant. For a complex sequence A=[a_0,a_1,...,a_{v-1}] of length v=dm we define the m-compressed sequence ... More

A class of cyclic $(v;k_1,k_2,k_3;λ)$ difference families with $v \equiv 3 \pmod{4}$ a primeNov 27 2015Jul 24 2016We construct several cyclic $(v;k_1,k_2,k_3;\lambda)$ difference families with $v\equiv3 \pmod{4}$ a prime and $\lambda=k_1+k_2+k_3-(3v-1)/4$. Such families can be used in conjunction with the well-known Paley-Todd difference sets to construct skew-Hadamard ... More

There is no circulant weighing matrix of order 60 and weight 36Jun 05 2014With the help of a computer, we prove the assertion made in the title.

Rational Orthogonal versus Real OrthogonalMar 16 2009The main question we raise here is the following one: given a real orthogonal n by n matrix X, is it true that there exists a rational orthogonal matrix Y having the same zero-pattern? We conjecture that this is the case and prove it for n<=5. We also ... More

Periodic Golay pairs of length 72Sep 21 2014Jan 27 2015We construct supplementary difference sets (SDS) with parameters $(72;36,30;30)$. These SDSs give periodic Golay pairs of length 72. No periodic Golay pair of length 72 was known previously. The smallest undecided order for periodic Golay pairs is now ... More

D-optimal matrices of orders 118, 138, 150, 154 and 174Aug 26 2014Jan 27 2015We construct supplementary difference sets (SDS) with parameters $(59;28,22;21)$, $(69;31,27;24)$, $(75;36,29;28)$, $(77;34,31;27)$ and $(87;38,36;31)$. These SDSs give D-optimal designs (DO-designs) of two-circulant type of orders 118,138,150,154 and ... More

New results on D-optimal MatricesMar 18 2011Jan 21 2012We construct a number of new (v;r,s;lambda) supplementary difference sets (SDS) with v odd and lambda = (r+s)-(v-1)/2. In particular, these give rise to D-optimal matrices of the four new orders 206, 242, 262, 482 constructed here for the first time.

Symmetric Hadamard matrices of order 116 and 172 existMar 13 2015Sep 28 2015We construct new symmetric Hadamard matrices of orders $92,116$, and $172$. While the existence of those of order $92$ was known since 1978, the orders $116$ and $172$ are new. Our construction is based on a recent new combinatorial array discovered by ... More

Some new orders of Hadamard and skew-Hadamard matricesJan 16 2013May 14 2013We construct Hadamard matrices of orders 4x251 = 1004 and 4x631 = 2524, and skew-Hadamard matrices of orders 4x213 = 852 and 4x631 = 2524. As far as we know, such matrices have not been constructed previously. The constructions use the Goethals-Seidel ... More

A SAT+CAS Approach to Finding Good Matrices: New Examples and CounterexamplesNov 13 2018We enumerate all circulant good matrices with odd orders divisible by 3 up to order 70. As a consequence of this we find a previously overlooked set of good matrices of order 27 and a new set of good matrices of order 57. We also find that circulant good ... More

Four-qubit pure states as fermionic statesSep 03 2013The embedding of the $n$-qubit space into the $n$-fermion space with $2n$ modes is a widely used method in studying various aspects of these systems. This simple mapping raises a crucial question: does the embedding preserve the entanglement structure? ... More

Charm bracelets and their application to the construction of periodic Golay pairsMay 28 2014Apr 06 2015A $k$-ary charm bracelet is an equivalence class of length $n$ strings with the action on the indices by the additive group of the ring of integers modulo $n$ extended by the group of units. By applying an $O(n^3)$ amortized time algorithm to generate ... More

Universal Subspaces for Local Unitary Groups of Fermionic SystemsJan 15 2013Mar 02 2013Let $\mathcal{V}=\wedge^N V$ be the $N$-fermion Hilbert space with $M$-dimensional single particle space $V$ and $2N\le M$. We refer to the unitary group $G$ of $V$ as the local unitary (LU) group. We fix an orthonormal (o.n.) basis $\ket{v_1},...,\ket{v_M}$ ... More

Canonical form of three-fermion pure-states with six single particle statesJun 11 2013Aug 09 2014We construct a canonical form for pure states in $\bwe^3(\bC^6)$, the three-fermion system with six single particle states, under local unitary (LU) transformations, i.e., the unitary group $\Un(6)$. We also construct a minimal set of generators of the ... More

Quadratic solitons as nonlocal solitonsMar 04 2003We show that quadratic solitons are equivalent to solitons of a nonlocal Kerr medium. This provides new physical insight into the properties of quadratic solitons, often believed to be equivalent to solitons of an effective saturable Kerr medium. The ... More

Fenchel-Nielsen coordinates on upper bounded pants decompositionsSep 26 2012Nov 16 2012Let $X_0$ be an infinite genus hyperbolic surface (whose boundary components, if any, are closed geodesics or punctures) which has an upper bounded pants decomposition. The length spectrum Teichm\"uller space $T_{ls}(X_0)$ consists of all surfaces $X$ ... More

A Thurston boundary for infinite-dimensional Teichmüller spacesMay 15 2018For a compact surface $X_0$, Thurston introduced a compactification of its Teichm\"uller space $\mathcal T(X_0)$ by completing it with a boundary $\mathcal{PML}(X_0)$ consisting of projective measured geodesic laminations. We introduce a similar bordification ... More

Subelliptic biharmonic mapsSep 29 2011We study subelliptic biharmonic maps, i.e. smooth maps from a compact strictly pseudoconvex CR manifold M into a Riemannian manifold N which are critical points of a certain bienergy functional. We show that a map is subelliptic biharmonic if and only ... More

Improving Schwarz Inequality in Inner Product SpacesSep 06 2017Some improvements of the celebrated Schwarz inequality in complex inner product spaces are given. Applications for n-tuples of complex numbers are provided.

Jacobi fields of the Tanaka-Webster connection on Sasakian manifoldsMay 15 2006We build a variational theory of geodesics of the Tanaka-Webster connection on a strictly pseudoconvex CR manifold.

Indefinite locally conformal Kaehler manifoldsMay 16 2006We study the basic geometric properties of an indefinite locally conformal Kaehler manifold.

On Some Discrete Inequalities in Normed Linear SpacesAug 09 2005Some sharp discrete inequalities in normed linear spaces are obtained. New reverses of the generalised triangle inequality are also given.

Reverses of the Schwarz Inequality in Inner Product Spaces Generalising a Klamkin-McLenaghan ResultAug 01 2005New reverses of the Schwarz inequality in inner product spaces that incorporate the classical Klamkin-McLenaghan result for the case of positive n-tuples are given. Applications for Lebesgue integrals are also provided.

Some Inequalities for Functions of Bounded Variation with Applications to Landau Type ResultsOct 18 2004Some inequalities for functions of bounded variation that provide reverses for the inequality between the integral mean and the p-norm are established. Applications related to the celebrated Landau inequality between the norms of the derivatives of a ... More

A General Divergence Measure for Monotonic Functions and Applications in Information TheoryJan 27 2004A general divergence measure for monotonic functions is introduced. Its connections with the f-divergence for convex functions are explored. The main properties are pointed out.

On the Chebyshev's Inequality for Weighted MeansNov 14 2003Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.

Bounding the Chebychev Functional for a Pair of Sequences in Inner Product SpacesSep 27 2003Some new bounds for the Chebychev functional of a pair of vectors in inner product spaces are pointed out. Reverses for the celebrated Jensen's inequality for convex functions defined on inner product spaces are given as well.

Advances in Inequalities of the Schwarz, Gruss and Bessel Type in Inner Product SpacesSep 22 2003Dec 01 2003The main aim of this monograph is to survey some recent results obtained by the author related to reverses of the Schwarz, triangle and Bessel inequalities. Some Gruss' type inequalities for orthonormal families of vectors in real or complex inner product ... More

On Bessel and Gruss Inequalities for Orthornormal Families in Inner Product SpacesMay 20 2003A new counterpart of Bessel's inequality for orthornormal families in real or complex inner product spaces is obtained. Applications for some Gruss type results are also provided.

A Generalisation of the Cassels and Greub-Reinboldt Inequalities in Inner Product SpacesJun 25 2003A generalisation of the Cassels and Greub-Reinboldt inequalities in complex or real inner product spaces and applications for isotonic linear functionals, integrals and sequences are provided.

Gruss Type Discrete Inequalities in Normed Linear Spaces, RevisitedJun 23 2003Some sharp inequalities of Gruss type for sequences of vectors in real or complex normed linear spaces are obtained. Applications for the discrete Fourier and Mellin transform are given. Estimates for polynomials with coefficients in normed spaces are ... More

The Median Principle for Inequalities and ApplicationsMar 27 2003The median principle is applied for different integral inequalities of Gruss and Ostrowski type.

A Fréchet topology on measured laminations and Earthquakes in the hyperbolic planeJun 04 2010We prove that the bijective correspondence between the space of bounded measured laminations $ML_b(\mathbb{H})$ and the universal Teichm\"uller space $T(\mathbb{H})$ given by $\lambda\mapsto E^{\lambda}|_{S^1}$ is a homeomorphism for the Fr\'echet topology ... More

The Quasi-hyperbolicity Constant of a Metric SpaceAug 12 2019We introduce the quasi-hyperbolicity constant of a metric space, a rough isometry invariant that measures how a metric space deviates from being Gromov hyperbolic. This number, for unbounded spaces, lies in the closed interval $[1,2]$. The quasi-hyperbolicity ... More

Symmetric Hadamard matrices of orders 268, 412, 436 and 604Mar 23 2018We construct many symmetric Hadamard matrices of small order by using the so called propus construction. The necessary difference families are constructed by restricting the search to the families which admit a nontrivial multiplier. Our main result is ... More

Negaperiodic Golay pairs and Hadamard matricesAug 04 2015Apart from the ordinary and the periodic Golay pairs, we define also the negaperiodic Golay pairs. (They occurred first, under a different name, in a paper of Ito.) If a Hadamard matrix is also a Toeplitz matrix, we show that it must be either cyclic ... More

Yang-Mills fields on CR manifoldsMay 15 2006We study pseudo Yang-Mills fields on a compact strictly pseudoconvex CR manifold.

Construction of symmetric Hadamard matrices of order $4v$ for $v=47,73,113$Oct 09 2017We continue our systematic search for symmetric Hadamard matrices based on the so called propus construction. In a previous paper this search covered the orders $4v$ with odd $v\le41$. In this paper we cover the cases $v=43,45,47,49,51$. The odd integers ... More

Turyn-type sequences: Classification, Enumeration and ConstructionJun 19 2012Turyn-type sequences, TT(n), are quadruples of {+,-1}-sequences (A;B;C;D), with lengths n,n,n,n-1 respectively, where the sum of the nonperiodic autocorrelation functions of A,B and twice that of C,D is a delta-function (i.e., vanishes everywhere except ... More

Syntax-aware Neural Semantic Role Labeling with SupertagsMar 12 2019Apr 03 2019We introduce a new syntax-aware model for dependency-based semantic role labeling that outperforms syntax-agnostic models for English and Spanish. We use a BiLSTM to tag the text with supertags extracted from dependency parses, and we feed these supertags, ... More

The B and Be States of the Star EM CepheusJun 15 2016We present eleven years of high-resolution, spectroscopic observations for the star EM~Cep. EM~Cep switches between B and Be star states, as revealed by the level of H$\alpha$ emission, but spends most of its time in the B~star state. EM~Cep has been ... More

Ruling out the orbital decay of the WASP-43bMar 03 2016We present 15 new transit observations of the exoplanet WASP-43b in the $i'$,$g'$, and $R$ filters with the 1.0-m telescopes of Las Cumbres Observatory Global Telescope (LCOGT) Network and the IAC80 telescope. We combine our 15 new light curves with 52 ... More

Quartic First-Order Methods for Low Rank MinimizationJan 30 2019Jun 10 2019We study a generalized nonconvex Burer-Monteiro formulation for low-rank minimization problems. We use recent results on non-Euclidean first order methods to provide efficient and scalable algorithms. Our approach uses geometries induced by quartic kernels ... More