It is well-known that for any integral domain R, the Serre conjecture ring R(X), i.e., the localization of the univariate polynomial ring R[X] at monic polynomials, is a Bezout domain of Krull dimension
We further the classification of rational surface singularities. Suppose (S, n, k) is a 3-dimensional strictly Henselian regular local ring of mixed characteristic (0, p > 5). We classify functions f for which S/(f) has an isolated rational singularity at ...
Background Many lower-limb exoskeletons have been developed to assist gait, exhibiting a large range of control methods. The goal of this paper is to review and classify these control strategies, that determine how these devices interact with the user. Met ...
Cloud platform services must simultaneously be scalable, meet low tail latency service-level objectives, and be resilient to a combination of software, hardware, and network failures. Replication plays a fundamental role in meeting both the scalability and ...
In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish local well-posedness of the Cauchy problem by a fixed point argument. Unlike ...
For any prime power q, Mori and Tanaka introduced a family of q-ary polar codes based on the q x q Reed-Solomon polarization kernels. For transmission over a q-ary erasure channel, they also derived a closed-form recursion for the erasure probability of ea ...
Let X be a finite set and let k be a commutative ring. We consider the k-algebra of the monoid of all relations on X, modulo the ideal generated by the relations factorizing through a set of cardinality strictly smaller than Card(X), called inessential rel ...
We investigate correspondence functors, namely the functors from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. They have various specific properties which do not hold for other types of functor ...
The special linear group G = SLn(Z[x(1), ... , x(k)]) (n at least 3 and k finite) is called the universal lattice. Let n be at least 4, and p be any real number in (1, infinity). The main result is the following: any finite index subgroup of G has the fixe ...
It is shown that the Euclidean group of translations, when treated as a Lie group, generates translations not only in Euclidean space but on any space, curved or not. Translations are then not necessarily vectors (straight lines); they can be any curve com ...
We introduce irregular product codes, a class of codes where each codeword is represented by a matrix and the entries in each row (column) of the matrix come from a component row (column) code. As opposed to standard product codes, we do not require that a ...
State machine replication reduces distributed to centralized computing. Any sequential service, modeled by a state machine, can be replicated over any number of processes and made highly available to all of them. At the heart of this fundamental reduction ...
The Mobius inversion formula of the free monogenic inverse semigroup is represented by the Mobius function for Cauchy product. In this short note we describe a Dirichlet analogue of this inverse semigroup. ...
Let K be a field with char(K) ≠ 2. The Witt-Grothendieck ring (K) and the Witt ring W (K) of K are both quotients of the group ring ℤ[𝓖(K)], where 𝓖(K) := K*/(K*)2 is the square class group of K. Since ℤ[𝓖(K)] is integra ...
We study annihilating polynomials and annihilating ideals for elements of Witt rings for groups of exponent 2. With the help of these results and certain calculations involving the Clifford invariant, we are able to give full sets of generators for the ann ...
This work concerns the study of Euclidean minima of maximal orders in central simple algebras. In the first part, we define the concept of ideal lattice in the non-commutative case. Let A be a semi-simple algebra over Q. An ideal lattice over A is a triple ...
This work is dedicated to developing algebraic methods for channel coding. Its goal is to show that in different contexts, namely single-antenna Rayleigh fading channels, coherent and non-coherent MIMO channels, algebraic techniques can provide useful tool ...
This thesis deals with the study of ideal lattices over number fields. Let K be a number field, which is assumed to be CM or totally real. An ideal lattice over K is a pair (I,b), where I is a fractional ideal of K and b : I × I → R is a symmetric positive ...
e analyze a special class of configurations with h sources and N receivers to demonstrate the throughput benefits of network coding and deterministic code design. We show that the throughput benefits network coding offers can increase proportionally to \sq ...
