Let k be a totally real field, and let A/k be an absolutely irreducible, polarized Abelian variety of odd, prime dimension whose endomorphism rings is non-trivial and is defined over k. Then the only strictly compatible families of abstract, absolutely irreducible representations of Gal(k/k) coming from A are tensor products of Tate twists of symmetric powers of two-dimensional λ-adic represent...

This note provides another proof for the convexity (strict convexity) of log det(I + KX) over the positive definite cone for any given positive semidefinite matrix K 0 (positive definite matrix K ≻ 0) and the strictly convexity of log det(K + X) over the positive definite cone for any given K 0. Equivalent optimization representation with linear matrix inequalities (LMIs) for the functions log ...

We prove the first lower bound for restricted read–once parity branching programs with unlimited parity nondeterminism where for each input the variables may be tested according to several orderings. Proving a superpolynomial lower bound for read–once parity branching programs is still a challenging open problem. The following variant of read–once parity branching programs is well–motivated. Le...

For k ∈ {1, 2, 3, . . . }, we construct an even compactly supported piecewise polynomial ψk whose Fourier transform satisfies Ak(1 + ω ) ≤ b ψk(ω) ≤ Bk(1 + ω ), ω ∈ R, for some constants Bk ≥ Ak > 0. The degree of ψk is shown to be minimal, and is strictly less than that of Wendland’s function φ1,k−1 when k > 2. This shows that, for k > 2, Wendland’s piecewise polynomial φ1,k−1 is not of minima...

This paper shows that one can be competitive with the kmeans objective while operating online. In this model, the algorithm receives vectors v1, . . . , vn one by one in an arbitrary order. For each vector vt the algorithm outputs a cluster identifier before receiving vt+1. Our online algorithm generates Õ(k) clusters whose k-means cost is Õ(W ∗) where W ∗ is the optimal k-means cost using k cl...

and Applied Analysis 3 2. The Sequence Space λ, p In this section, we define the sequence space λ, p and prove that this sequence space according to its paranorm is complete paranormed linear space. In 1 , Mursaleen and Noman defined the matrix Λ λnk ∞ n,k 0 by λnk ⎧ ⎨ ⎩ λk − λk−1 λn 0 ≤ k ≤ n 0 k > n , 2.1 where λ λk ∞ k 0 is a strictly increasing sequence of positive reals tending to ∞, that ...

We provide new interpretations for a subset of Raney numbers, involving threshold sequences and Motzkin-like paths with long up down steps. Given three integers n,k,ℓ such that n≥1,k≥2 0≤ℓ≤k−2, (k,ℓ)-threshold sequence length n is any strictly increasing S=(s1s2…sn) ki≤si≤kn+ℓ. These are in bijection the (ℓ+1)-tuples k-ary trees total internal nodes. prove this result using counting arguments b...

The minimizers of the anisotropic fractional isoperimetric inequality with respect to a convex body $ K in \mathbb{R}^n are shown be equivalent star bodies whenever is strictly and unconditional. From this Pólya-Szeg? principle for seminorms derived by using symmetrization bodies.

In the k-mismatch problem we are given a pattern of length n and text must find all locations where Hamming distance between is at most k. A series recent breakthroughs have resulted in an ultra-efficient streaming algorithm for this that requires only $$\mathcal {O}(k \log \frac{n}{k})$$ space {O}(\log \frac{n}{k} (\sqrt{k k} + ^3 n))$$ time per letter (Clifford, Kociumaka, Porat, SODA 2019). ...

Let G be the Klein four-group and let k an arbitrary field of characteristic 2. A classification indecomposable kG-modules is known. We calculate relative cohomology groups Hχi(G,N) for every kG-module N, where χ set proper subgroups in G. This extends work Pamuk Yalcin to with non-trivial coefficients. also show that all cup products strictly positive degree Hχ*(G,k) are trivial.