Odd Characteristics Research Articles

On a certain duality of Néron-Severi lattices of supersingular K3 surfaces

Let X and Y be supersingular K3 surfaces defined over an algebraically closed field. Suppose that the sum of their Artin invariants is 11. Then there exists a certain duality between their Neron–Severi lattices. We investigate geometric consequences of this duality. As an application, we classify genus one fibrations on supersingular K3 surfaces with Artin invariant 10 in characteristic 2 and 3, and give a set of generators of the automorphism group of the nef cone of these supersingular K3 surfaces. The difference between the automorphism group of a supersingular K3 surface X and the automorphism group of its nef cone is determined by the period of X. We define the notion of genericity for supersingular K3 surfaces in terms of the period, and prove the existence of generic supersingular K3 surfaces in odd characteristics for each Artin invariant larger than one.

On the Decomposition Numbers of Steinberg's Triality Groups 3 D 4(2 n ) in Odd Characteristics

We determine the ℓ-modular decomposition matrices of Steinberg's triality groups 3 D 4(2 n ) for all primes ℓ ≠ 2 except for some entries in the unipotent characters. As an application, we classify all absolutely irreducible representations of 3 D 4(2 n ) in non-defining characteristic up to a certain degree.

On the set of integral solutions of the Pell equation in global function fields

We give a complete description of the structure of the set of all integral solutions to Pell equations in function fields over any finite field, both even and odd characteristics.

ON ISOTOPISMS OF COMMUTATIVE PRESEMIFIELDS AND CCZ-EQUIVALENCE OF FUNCTIONS

A function F from Fpnto itself is planar if for any [Formula: see text] the function F(x+a)-F(x) is a permutation. CCZ-equivalence is the most general known equivalence relation of functions preserving planar property. This paper considers two possible extensions of CCZ-equivalence for functions over fields of odd characteristics, one proposed by Coulter and Henderson and the other by Budaghyan and Carlet. We show that the second one in fact coincides with CCZ-equivalence, while using the first one we generalize one of the known families of PN functions. In particular, we prove that, for any odd prime p and any positive integers n and m, the indicators of the graphs of functions F and F' from Fpnto Fpmare CCZ-equivalent if and only if F and F′ are CCZ-equivalent.We also prove that, for any odd prime p, CCZ-equivalence of functions from Fpnto Fpm, is strictly more general than EA-equivalence when n ≥ 3 and m is greater or equal to the smallest positive divisor of n different from 1.

Microwave permittivity of leaf using an Ag thick-film microstrip resonator

The X-band microwave dielectric constant, dielectric loss and the conductivity of the leaves of four different plants were measured from even and odd mode resonance characteristics of an Ag thick-film microstrip straight resonator, due to the perturbation caused by leafy vegetation as an overlay. Using the changes in the frequency response, the moisture-dependent X-band microwave properties of the leaves of Ficus Bengalensis, Ficus Religiosa, Acalypha Wilkensiana, and Acalypha Hispidia have been calculated. The permittivity obtained depends on the position of the overlay and moisture content. A partial overlay method might be a low-cost alternative for dielectric characterisation of biomaterials since a very small size of leaf is needed.

Infinite families of new semifields

We construct six new infinite families of finite semifields, all of which are two-dimensional over their left nuclei. We give constructions for both even and odd characteristics when the left nucleus has odd dimension over the center. The characteristic is odd in the one family in which the left nucleus has even dimension over the center. Spread sets of linear maps are used in all the constructions.

Gradual and complete delivery of a hydatid cyst of the brain through a single burr hole, a wrong happening!

Cerebral hydatidosis is a rare larval infection of the central nervous system affecting mostly the children and young adults. The authors report a case of a 5-year-old girl harboring a large right frontoparietal hydatid cyst. The imaging studies were not diagnostic for 'cerebral hydatidosis' and were interpreted as 'brain abscess'. Attempting for simple cannulation of the lesion through a burr hole drained a clear fluid. The cannula was removed promptly but the cyst wall came out little by little through the hole in a single piece which turned out to be the entire wall of a hydatid cyst. She was treated by antihelmintic medications for 6 months and there has been no sign of recurrence after a year. Odd paraclinical imaging characteristics and unique accidental surgical event makes this case the first reported pediatric brain hydatidosis with spontaneous complete delivery of the cyst through a single burr hole which can certainly be considered a wrong attempt if undertaken intentionally.

Wahl’s conjecture holds in odd characteristics for symplectic and orthogonal Grassmannians

Abstract It is shown that the proof by Mehta and Parameswaran of Wahl’s conjecture for Grassmannians in positive odd characteristics also works for symplectic and orthogonal Grassmannians.

Decomposition numbers of non-principal blocks of [formula omitted] for characteristic 3

In this paper, the decomposition numbers of the non-principal blocks of the largest Janko group J 4 [Z. Janko, A new finite simple group of order 86,775,571,046,077,562,880 which possesses M 24 and the full covering group of M 22 as subgroups, J. Algebra 42 (1976) 564-596] for characteristic 3 are determined up to some unknown parameters. We are also concerned with the decomposition numbers of maximal 2-local subgroups of J 4 in odd characteristics.

Poisson sigma model with branes and hyperelliptic Riemann surfaces

We derive the explicit form of the superpropagators in the presence of general boundary conditions (coisotropic branes) for the Poisson sigma model. This generalizes the results presented by Cattaneo and Felder [“A path integral approach to the Kontsevich quantization formula,” Commun. Math. Phys. 212, 591 (2000)] and Cattaneo and Felder [“Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model,” Lett. Math. Phys. 69, 157 (2004)] for Kontsevich’s angle function [Kontsevich, M., “Deformation quantization of Poisson manifolds I,” e-print arXiv:hep.th/0101170] used in the deformation quantization program of Poisson manifolds. The relevant superpropagators for n branes are defined as gauge fixed homotopy operators of a complex of differential forms on n sided polygons Pn with particular “alternating” boundary conditions. In the presence of more than three branes we use first order Riemann theta functions with odd singular characteristics on the Jacobian variety of a hyperelliptic Riemann surface (canonical setting). In genus g the superpropagators present g zero mode contributions.

Joining linguistic and statistical methods for Spanish-to-Basque speech translation

The goal of this work is to develop a text and speech translation system from Spanish to Basque. This pair of languages shows quite odd characteristics as they differ extraordinarily in both morphology and syntax, thus, attractive challenges in machine translation are involved. Nevertheless, since both languages share official status in the Basque Country, the underlying motivation is not only academic but also practical. Finite-state transducers were adopted as basic translation models. The main contribution of this work involves the study of several techniques to improve probabilistic finite-state transducers by means of additional linguistic knowledge. Two methods to cope with both linguistics and statistics were proposed. The first one performed a morphological analysis in an attempt to benefit from atomic meaningful units when it comes to rendering the meaning from one language to the other. The second approach aimed at clustering words according to their syntactic role and used such phrases as translation unit. From the latter approach phrase-based finite-state transducers arose as a natural extension of classical ones. The models were assessed under a restricted domain task, very repetitive and with a small vocabulary. Experimental results shown that both morphological and syntactical approaches outperformed the baseline under different test sets and architectures for speech translation.

Odd characteristics of Au film on pentacene

Anomalies of Au film formed on the pentacene surface are investigated as a counterpart of pentacene/Au structure. The Au film is found to contain pentacene derivatives originated from the pentacene layers, and it is composed of grains of various sizes formed as the Au thickness increases. The authors suggest that it is this abundance of peculiarities of the Au film that accounts for the attenuated density of states in the valence band. Deformation of Au grains is accompanied by the lift of the pentacene layers, which, in turn, brings about the device failure.

Appendicitis at Kenyatta National Hospital, Nairobi

Appendicitis still remains a diagnostic challenge particularly in women and extremes of age. The incidence of appendicectomy for suspected appendicitis is higher but declining in the developed countries in contrast with a low but increasing incidence in Africa. To describe the characteristics of appendicitis at Kenyatta National Hospital, with emphasis on epidemiological oddities. A prospective descriptive study. Kenyatta National Hospital, a 2000 bed teaching and referral hospital in Nairobi, Kenya One hundred and eighty nine patients managed for suspected acute appendicitis between July 2000 and June 2001. There were 116 males and 73 females. The peak incidence was in the third decade. Sixty four percent of patients were below 30 years of age. The elderly (< 60 years of age) accounted for 1.6% of cases. The rate of false appendicectomy was 18.0%. This rate of negative appendicectomies was 12.9% for males and 30.1% for females. The rate of perforation/gangrene was 29.7%. Hospital stay averaged 6.4 days. Overall morbidity was 12.3%. It was 19.4% in perforated appendicitis and 7.6% in non-perforated appendicitis. There was no mortality. The incidence of appendicitis has increased at Kenyatta National Hospital over the last 30 years. The disease is common in men in their third decade. These odd characteristics warrant further investigations.

A Weil Descent Attack against Elliptic Curve Cryptosystems over Quartic Extension Fields

This paper proposes a Weil descent attack against elliptic curve cryptosystems over quartic extension fields. The scenario of the attack is as follows: First, one reduces a DLP on a Weierstrass form over the quartic extention of a finite field k to a DLP on a special form, called Scholten form, over the same field. Second, one reduces the DLP on the Scholten form to a DLP on a genus two hyperelliptic curve over the quadratic extension of k. Then, one reduces the DLP on the hyperelliptic curve to one on a Cab model over k. Finally, one obtains the discrete-log of original DLP by applying the Gaudry method to the DLP on the Cab model. In order to carry out the scenario, this paper shows that many of elliptic curve discrete-log problems over quartic extension fields of odd characteristics are reduced to genus two hyperelliptic curve discrete-log problems over quadratic extension fields, and that almost all of the genus two hyperelliptic curve discrete-log problems over quadratic extension fields of odd characteristics come under Weil descent attack. This means that many of elliptic curve cryptosystems over quartic extension fields of odd characteristics can be attacked uniformly.

On monomial graphs of girth eight

Let e be a positive integer, p be an odd prime, q = p e , and F q be the finite field of q elements. Let f 2 , f 3 ∈ F q [ x , y ] . The graph G = G q ( f 2 , f 3 ) is a bipartite graph with vertex partitions P = F q 3 and L = F q 3 , and edges defined as follows: a vertex ( p ) = ( p 1 , p 2 , p 3 ) ∈ P is adjacent to a vertex [ l ] = [ l 1 , l 2 , l 3 ] if and only if p 2 + l 2 = f 2 ( p 1 , l 1 ) and p 3 + l 3 = f 3 ( p 1 , l 1 ) . Motivated by some questions in finite geometry and extremal graph theory, we ask when G has no cycle of length less than eight, i.e., has girth at least eight. When f 2 and f 3 are monomials, we call G a monomial graph. We show that for p ⩾ 5 , and e = 2 a 3 b , a monomial graph of girth at least eight has to be isomorphic to the graph G q ( x y , x y 2 ) , which is an induced subgraph of the classical generalized quadrangle W ( q ) . For all other e, we show that a monomial graph is isomorphic to a graph G q ( x y , x k y 2 k ) , with 1 ⩽ k ⩽ ( q − 1 ) / 2 and satisfying several other strong conditions. These conditions imply that k = 1 for all q ⩽ 10 10 . In particular, for a given positive integer k, the graph G q ( x y , x k y 2 k ) can be of girth eight only for finitely many odd characteristics p.

Direct-coupled microwave filters with single and dual stopbands

This paper presents new ideas for the design and implementation of microwave filters with single and dual stopbands. They can be realized with waveguide, coaxial, dielectric resonators, or in a planar technology. The new methods represent an advance over present methods in that the resonators are direct coupled, thus avoiding the need for transmission line phase lengths between resonator stubs that tend to degrade performance due to their dispersion and are difficult to adjust during tuning. Three bandstop (BS) configurations are presented. The first will accommodate even or odd characteristics and also asymmetric responses, although some negative or diagonal cross-couplings will be needed. The second resembles the cul-de-sac configuration for bandpass filters and needs no diagonal or negative couplings even for asymmetric characteristics. The third is an application of the cul-de-sac synthesis technique to dual-band bandstop (DBBS) filters. All these BS designs are very similar to regular bandpass filters in their design and realization. The design of a DBBS filter is presented and compared with an equivalent bandpass filter to demonstrate its advantages. Finally, the simulated and measured results of a fourth-degree BS filter design in the novel cul-de-sac configuration are presented.

Speeding up Scalar Multiplication in Genus 2 Hyperelliptic Curves with Efficient Endomorphisms

This paper proposes an efficient scalar multiplication algorithm for hyperelliptic curves, which is based on the idea that efficient endomorphisms can be used to speed up scalar multiplication. We first present a new Frobenius expansion method for special hyperelliptic curves that have Gallant-Lambert-Vanstone (GLV) endomorphisms. To compute kD for an integer k and a divisor D, we expand the integer k by the Frobenius endomorphism and the GLV endomorphism. We also present improved scalar multiplication algorithms that use the new expansion method. By our new expansion method, the number of divisor doublings in a scalar multiplication is reduced to a quarter, while the number of divisor additions is almost the same. Our experiments show that the overall throughputs of scalar multiplications are increased by 15.6 to 28.3 % over the previous algorithms when the algorithms are implemented over finite fields of odd characteristics.

Recurrent methods for constructing irreducible polynomials over [formula omitted] of odd characteristics, II

In this paper computationally easy explicit constructions of sequences of irreducible and normal monic polynomials over finite fields of odd characteristic are presented.

Show me the genes – I will tell you who/how to treat!

Show me the genes – I will tell you who/how to treat!

The stack of Potts curves and its fibre at a prime of wild ramification

In this note we study the modular properties of a family of cyclic coverings of P 1 of degree N, in all odd characteristics. We compute the moduli space of the corresponding algebraic stack over Z[1/2] , as well as the Picard groups over algebraically closed fields. We put special emphasis on the study of the fibre of the stack at a prime of wild ramification; in particular we show that the moduli space has good reduction at such a prime.