Maximal AMDS codes

Complete (n, k)-arcs in PG(k − 1, q) and projective (n, k) _q -AMDS codes that admit no projective extensions are equivalent objects. We show that projective AMDS codes of reasonable length admit only linear extensions. Thus, we are able to prove the maximality of many known linear AMDS codes. At the same time our results sharply limit the possibilities for constructing long nonlinear AMDS codes. We also show that certain short linear AMDS codes are maximal. Central to our approach is the Bruen–Silverman model of linear codes first introduced in Alderson (On MDS codes and Bruen–Silverman codes. Ph.D. Thesis, University of Western Ontario, 2002) and Alderson et al. (J. Combin. Theory Ser. A 114(6), 1101–1117, 2007). The authors acknowledge support from the N.S.E.R.C. of Canada.     

Group codes on certain algebraic curves with many rational points

We construct a series of algebraic geometric codes using a class of curves which have many rational points. We obtain codes of lengthq ² over _q , whereq = 2q ₀ ² andq ₀ = 2 ⁿ , such that dimension + minimal distance q ² + 1 – q ₀ (q – 1). The codes are ideals in the group algebra _q [S], whereS is a Sylow-2-subgroup of orderq ² of the Suzuki-group of orderq ² (q ² + 1)(q – 1). The curves used for construction have in relation to their genera the maximal number of GF _q -rational points. This maximal number is determined by the explicit formulas of Weil and is effectively smaller than the Hasse—Weil bound.Supported by Deutsche Forschungsgemeinschaft while visiting Essen University     

The Characters of a Sylow p-Subgroup of the Group G2(pn), p≠2, 3

 We compute the irreducible complex characters of a Sylow p-subgroup of the Chevalley group G ₂(q), q=p ⁿ , p≠2, 3 and show that the non linear irreducible characters are induced from linear characters of subgroups of order q ⁵ and q ⁴. Received April 6, 1995     

Primitive Polynomials over Finite Fields of Characteristic Two

Let F _q be a finite field of characteristic two. We prove that for any given element a F _q , there exists a primitive polynomial of degree n over F _q with the m-th (0<m<n) coefficient _m =a when n7, n is odd. Keywords:Finite field, Primitive polynomial, Galois ring, Character sums over Galois ring, The sieve method.     

On the Lattice Structure of Pseudorandom Numbers Generated over Arbitrary Finite Fields

Marsaglia's lattice test for congruential pseudorandom number generators modulo a prime is extended to a test for generators over arbitrary finite fields. A congruential generator η₀,η₁,…, generated by η _n =g(n), n = 0, 1,…, passes Marsaglia's s-dimensional lattice test if and only if s≤ deg(g). It is investigated how far this conditin holds true for polynomials over arbitrary finite fields F _q , particularly for polynomials of the form g _d (x)=α(x+β) ^d +γ, α, β, γ∈F _q , α≠ 0, 1 ≤d≤q− 1. Received: December 13, 1999; revised version: November 17, 2000     

Cryptanalysis of ‘Less Short’ RSA Secret Exponents

 In some applications of RSA, it is desirable to have a short secret exponent d. Wiener [6], describes a technique to use continued fractions (CF) in a cryptanalytic attack on an RSA cryptosystem having a ‘short’ secret exponent. Let n=p ⋅ q be the modulus of the system. In the typical case that G=gcd(p−1, q−1) is small. Wiener’s method will give the secret exponent d when d does not exceed (approximately) n ^1/4. Here, we describe a general method to compute the CF-convergents of the continued fraction expansion of the same number as in Wiener (which has denominator d ⋅ G) up to the point where the denominator of the CF-convergent exceeds approximately n ^1/4. When d<n ^1/4 this technique determines d, p, and q as does Wiener’s method. For larger values of d there is still information available on the secret key. An estimate is made of the remaining workload to determine d, p and q. Roughly speaking this workload corresponds to an exhaustive search for about 2r+8 bit, where r=ln₂ d/n ^1/4. Received: September 30, 1996; revised version: March 7, 1997     

Frontiers and symmetries of dynamical systems

The frontiers of boundedness ? _b of the orbits of dynamical systems X defined on ? ⁿ are studied. When X is completely integrable some topological properties of ? _b are found and, in certain cases, ? _b is localized with the help of symmetries of X. Several examples in dimensions 2 and 3 are provided. In case the number of known first integrals of the vector field X is less than n ? 1, an interesting connection of ? _b with the frontier of boundedness of the level-sets of the first integrals of X is proved. This result also applies to Hamiltonian systems.     

Paramagnetic susceptibility and ultrasonic attenuation of itinerant antiferromagnetism above the Neel temperature

Making use of the two-band model of the itinerant antiferromagnetism, we calculate the wave-vector-dependent paramagnetic susceptibility (i.e., the fluctuation propagator of the order parameter) and the ultrasonic attenuation coefficient above the Neel temperatureT _N .We distinguish two regions depending on the degree of the nesting between the electron and the hole bands. The degree of the nesting is characterized byH, which measures the difference of the Fermi radii of the electron and the hole bands. WhenH is less than the critical nestingH*, the fluctuation is of the diffusion type indicating the transition into the commensurate spin density wave (CSDW) state; the fluctuation propagator diverges atT=T _N forq=0 (the paramagnetic susceptibility diverges forq=G _i /2;G _i are the reciprocal lattice vectors) whereq is the wave number vector. WhenH>H*, on the other hand, the fluctuation propagator diverges atT=T _N ,on the sphere in the wave vector space with the radiusq ₀,signalling the transition into the incommensurate spin wave (ISDW) state; the paramagnetic susceptibility diverges now forq=(G _i /2)+q, where |q|=q ₀.The attenuation coefficient is much enhanced due to the spin fluctuation nearT _N . We find that the attenuation coefficient of the longitudinal sound wave diverges atT=T _N as ^–3/2 forHH* and ^–5/2 forH>H*, where =(T/T _N )–1. The latter prediction is in reasonable agreement with the recent measurement of the attenuation coefficient in pure Cr by Imai and Sawada.     

Nonlinear viscoelasticity and relaxation phenomena of polymer solids

Summary The specific Helmholtz free energy of nonlinear viscoelastic isotropic polymer solids is assumed to be a separable, symmetric function along three orthogonal principal strain directions, i.e.=( ₁,q _n ⁽¹⁾)+( ₂,q _n ⁽²⁾)+( ₃,q _n ⁽³⁾), where the _r (r=1, 2, 3) are three principal stretch ratios and theq _n ( ^r ) are a set of internal state variables. It is shown that, by using this postulated form of the free energy function, one can readily characterize the mechanical response of viscoelastic polymer solids.

---

Nichtlineare Viskoelastizität und Relaxationserscheinungen in festen Polymeren

Zusammenfassung Die spezifische Helmholtzsche freie Energie nichtlinear-viskoelastischer, isotroper, fester Polymere wird als separable, symmetrische Funktion der Form=( ₁,q _n ⁽¹⁾)+( ₂,q _n ⁽²⁾)+( ₃,q _n ⁽³⁾) angenommen mit den drei Hauptdehnungsverhältnissen _r (r=1, 2, 3) und inneren Zustandsvariablenq _n ( ^r ). Es wird gezeigt, daß dann das mechanische Verhalten der viskoelastischen festen Polymere schnell charakterisiert werden kann.

---

---

This represents the results of one phase of research being carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract NAS 7-100, sponsored by the National Aeronautics and Space Administration.     

Satellite peaks in the scattering of p-polarized light from a randomly rough film on a perfectly conducting substrate

Abstract

The diffuse scattering of p-polarized light from a one-dimensional, randomly rough dielectric film deposited on a planar, perfectly conducting surface is studied by means of small-amplitude perturbation theory. The dielectric constant ε_d and the thickness d of the dielectric film are chosen in such a way that in the absence of roughness the scattering system supports N (≥ 2) guided modes whose wavenumbers are q ₁ (ω), …,q _N(ω) at the frequency ω of the light incident at an angle θ_o. We investigate the occurrence of satellite peaks, in addition to the enhanced back-scattering peak, in the angular distribution of the intensity of the diffusely scattered light, at angles θ_s(n, m) given by sin θ_s(n, m)= ? sin θ₀± (c/ω) [Q_n(ω) ? q_m(ω)] for n, m=1, …, N(n ≠ m). These satellite peaks are multiple-scattering effects due to degenerate timereversal symmetry.     

Heat transfer through subcooled He I layer from distributed heat source in a pressurized He II channel

The subcooled He I layer, in contact with a large heated surface in a channel filled with the pressurized superfluid He II (He II_p), expands the non-boiling region above the Kapitza region up to q_n, above which nucleate boiling sets in. As the bath temperature decreases, q_n is increased more rapidly than q_λ at which the superfluidity is broken at the centre of the heated surface. The value of q_n is increased as the channel gap increases, and is independent of the channel orientation as well as q_λ. Metastabilization of superconducting coils may be enhanced by taking the non-boiling limit q_n into account.     

A Nonextensive Approach to Bose-Einstein Condensation of Trapped Interacting Boson Gas

In the Bose-Einstein condensation of interacting atoms or molecules such as ⁸⁷Rb, ²³Na and ⁷Li, the theoretical understanding of the transition temperature is not always obvious due to the interactions or zero point energy which cannot be exactly taken into account. The S-wave collision model fails sometimes to account for the condensation temperatures. In this work, we look at the problem within the nonextensive statistics which is considered as a possible theory describing interacting systems. The generalized energy U _q and the particle number N _q of boson gas are given in terms of the nonextensive parameter q. q>1 (q<1) implies repulsive (attractive) interaction with respect to the perfect gas. The generalized condensation temperature T _cq is derived versus T _c given by the perfect gas theory. Thanks to the observed condensation temperatures, we find q≈0.1 for ⁸⁷Rb atomic gas, q≈0.95 for ⁷Li and q≈0.62 for ²³Na. It is concluded that the effective interactions are essentially attractive for the three considered atoms, which is consistent with the observed temperatures higher than those predicted by the conventional theory.      

An enumeration formula for certain irreducible polynomials with an application to the construction of irreducible polynomials over the binary field

We establish a formula for the number of irreducible polynomialsf(x) over the binary fieldF ₂ of given degreen 2 for which the coefficient ofx ^n-1 and ofx is equal to 1. This formula shows that the number of such polynomials is positive for alln 2 withn 3. These polynomials can be applied in a construction of irreducible self-reciprocal polynomials overF ₂ of arbitrarily large degrees.     

Lattice Structure and Linear Complexity of Nonlinear Pseudorandom Numbers

 It is shown that a q-periodic sequence over the finite field F _q passes an extended version of Marsaglia's lattice test for high dimensions if and only if its linear complexity is large. The consequences of this result for nonlinear and inversive pseudorandom number generators are worked out. Received: October 2, 2001 Keywords: Pseudorandom number generator, Nonlinear method, Inversive method, Linear complexity, Marsaglia's lattice test.     

Few-phonon structure functions for liquid helium II

A semiphenomenological method is formulated for calculating the Fourier transforms of the few-body distribution functions—the few-phonon liquid structure functionsS _s(q ₁,...,q _s–1)—on the basis of a functional Ansatz independent of a superposition approximation. The two-phonon functionS ₂ (q)=S(q) is calculated and compared with the experimentalS(q) to determine the parameters of the functional Ansatz. The procedure is to writeS _s in second-quantized form, to transfer from particle operatorsa _k to operators _k , and then to take expectation values with respect to the ground state |0) of the _k 's. The transformation is, fork0, a _k =(1+v _k ² )^1/2 _k +v _k ² _–k ⁺ . Fork=0, a ₀ ⁺ a₀|0) is written in terms of the othera _k 's as effectively the most general possible expression. This expression is nonlinear and involves arbitrary parametric functions subject to the restrictions that(0|a ₀ ⁺ a₀|0)=N₀, and that theS _s have the proper physical properties. Thes-body functionS _s is then expressed as a functional ofv _k , ands–1 parametric functionsc ₂,...,c_s–1 arising from the expression fora ₀ ⁺ a₀|0). The functionsc ₃, c₄,..., contribute only for smallq. A simple algebraic expression forv _k , containing only a few parameters, is found which yields agreement with experiment forS(q) to within the 10% calculational error. The relative number of particles in the zero-momentum staten ₀ , calculated as a consistency check, turns out to be equal to 0.2. Having determinedv _k andc ₂, S₃ can then be evaluated in a straight-forward manner.S ₃ is explicitly displayed as a functional ofv _k , c₂, andc ₃. It is shown thatc ₃(k, k) can be chosen so thatS ₃(s,p) has the correct known behavior for smalls.     

An efficient access control scheme for files protection

Abstract

A dynamic access control mechanism suitable for hardware implementation is proposed. Each file is safeguarded by q lock values, where q is number of the possible access classes. The access right of a user to some file can be revealed very efficiently. In addition, dynamic operations such as changing a privilege value, insertion or deletion of a user, and insertion or deletion of a file can be done easily. Compared to Wu and Hwangs’ and Chang's methods, the computation of lock values is simple and the verification of an access request is quite efficient. The storage required is proportional to m?n which is less than that of the above‐mentioned methods, where m is the number of users and n is the number of files.     

Extraction of Lanthanide(III) Nitrates from Aqueous Solutions with Mixtures n-Octanol-Decane, Tri-n-butyl Phosphate-n-Octanol, and Diisoamyl Methylphosphonate-n-Octanol

Extraction of lanthanide(III) (La-Eu) nitrates from aqueous solutions with 3.15 M solution of octanol (ROH) in n-decane (extractant 1), 2.02 M solution of diisoamyl methylphosphonate (S = DIAMP) in n-octanol (extractant 2), and 1.83 M solution of tri-n-butyl phosphate (S = TBP) in n-octanol (extractant 3) was studied at T = 298.15 K. The extraction of lanthanide(III) nitrates with extractant 1 at C(aq) > 0.6 M is described by the equation of the heterogeneous reaction Ln³⁺(aq) + 3NO ₃ ⁻ (aq) + 4ROH(o) = [Ln(NO₃)₃ ⋅ (ROH)₄](o). The extraction of Ln(III) nitrates with extractants 2 and 3 involves the reaction described above in combination with the heterogeneous reaction Ln³⁺(aq) + 3NO ₃ ⁻ (aq) + 3S(o) = [Ln(NO₃)₃(S)₃](o) and the homogeneous reaction ROH(o) + S(o) = [ROH ⋅ S](o), where S is DIAMP or TBP. The electronic absorption and IR spectra of Nd(III) and Pr(III) nitrates in n-octanol and n-octanol-TBP mixtures were analyzed.__________Translated from Radiokhimiya, Vol. 47, No. 3, 2005, pp. 245–251.Original Russian Text Copyright © 2005 by Kudrova, Keskinov, Pyartman.     

On the Extendibility of Near-MDS Elliptic Codes

The Main Conjecture on maximum distance separable (MDS) codes states that, except for some special cases, the maximum length of a q-ary linear MDS code of is q+1. This conjecture does not hold true for near maximum distance separable codes because of the existence of q-ary near-MDS elliptic codes having length bigger than q+1. An interesting related question is whether a near-MDS elliptic code may be extended to a longer near-MDS code. In this paper we prove some non-extendibility results for certain near-MDS elliptic codes.     

The enhancement of spontaneous and induced transition rates by a Bose-Einstein condensate

Abstract

In this paper, an exactly solved model for the emission by N atoms is presented, the spontaneous and induced transition rates obtained, are enhanced by a factor which is proportional to the number of atoms n in the volume Λ³(2π²) (A is the transition wavelength of the atom) and dependent on the de-Broglie wavelength Λ_B in a more complicated way.     

Construction of irreducible polynomials using cubic transformation

The transformationf(x)f(x ³–3x) is studied. We show that for allF _q of characteristic >3 andn1, there existsf(x)F _q [x] of degreen which generates an infinite sequence of irreducible polynomials of degree 3 ⁱ n by the iteration of this transformation.