Remark on cellular automata and shift preserving maps

The main goal of this work is to show an extension of well known Hedlund’s theorem which states that in the Cantor topology the cellular automata are the continuous shift preserving maps. This extension maintains the topological structure and uses the concept of barriers of Set Theory to generalize the notion of local rule in the definition of cellular automata.     

Optimal thermal phase shift filters

In passive solar heating architecture the daily heat wave enters the structure, is attenuated in amplitude, and is shifted in phase. This poses the problem of minimizing the attenuation without changing the phase. Heat flow can be simulated by an RC electrical filter with grounded capacitors. This paper treats the problem of selecting the capacitors of such a filter to minimize the attenuation across a resistive load. An algorithm is developed and a graph of attenuation versus load is plotted when the phase lag of the inside temperature is twelve hours.     

Remark on the standard identity

It is proved that the standard identity of degree n implies all Capelli identities of some order m depending on n.Translated from Matematicheskie Zametki, Vol. 23, No. 5, pp. 753–757, May, 1978.     

Remark on cyclic vectors in the Dirichlet space

We give a new proof for the conjecture: if g   is a cyclic vector in Dirichlet space and if |f(z)|?|g(z)|$|f(z)|?|g(z)|$ for all points, then f is cyclic.     

Remark on the weierstrass points on curves

We give a treatment of the Weiertrass points of curves which is a little different from the treatment by Laksov. We introduce the notion of theith weight which makes the treatment easier and gives an algorithm for computing the gap sequence of an effective divisor and the weight at a point. Supported in part by NNSF of China.     

Schwarz引理的一个注记

本文中,基于幅角原理和同论理论紧密联系的想法,我们对单复变中经典的Sdlwarz引理给出了一个新的证明.同时,运用同样的方法,我们把Schwarz引理推广到亚纯函数和多连通区域的情形.     

A Remark on the Rank Conjecture

We prove a result about the action of -operations on the homology of linear groups. We use this to give a sharper formulation of the rank conjecture as well as some shorter proofs of various known results. We formulate a conjecture about how the sharper formulation of the rank conjecture together with another conjecture could give rise to a different point of view on the isomorphism between and K_n^{(p)} (F)$ for an infinite field F, and we prove part of this new conjecture.     

Remark on the Strichartz estimates in the radial case

We prove up to an endpoint the full radial Strichartz estimates for the Schrödinger-type equation in the radial case. Our results improve the one obtained in Guo and Wang (2011) [2]. The main ingredient is that we exploit some orthogonality to overcome the logarithmic divergence.     

Remark on the Lebesgue constant in the Rogosinski Kernel

For every n, we compute the Lebesgue constant of Rogosinski kernel with any preassigned accuracy.     

Remark on Kreisel's conjecture

At the end of the 60's, Kreisel conjectured that formal arithmetics admit infinite induction rules if the lengths of proofs of their premises are uniformly bounded by the same number. By the length of a proof we mean the number of applications of axioms and rules of inference. In this article we construct a theory R ^* with a finite number of specific axioms. The language of R ^* contains a constant 0, a unary function symbol, equality, and ternary predicates for addition and multiplication. It is proved that for any consistent axiomatizable extensionR^* it is possible to find a formula A(a) that satisfies the following conditions: a) xA(x) cannot be derived in; b) for any n the length of the proof of the formula A(0⁽ⁿ⁾) is no greater than c₁[log₂ (n+1)]+c₂, where the constants c₁ and c₂ are independent of n. Here the expression 0⁽ⁿ⁾ indicates 0 with n primes.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Institua im. V. A. Steklova Akademii Nauk SSSR, Vol. 176, pp. 118–126, 1989.     

Remark on the Hopf Bifurcation Theorem

A simple generalization of the Hopf Bifurcation Theorem for scalar higher order ordinary differential equations is suggested. We study the degenerate case where several roots of the characteristic polynomial cross the imaginary axis at the same point for some value λ₀ of the parameter λ. The main result is that if N₁ roots cross the imaginary axis from the left to the right and N₂ roots cross it from the right to the left, then λ₀ is a Hopf bifurcation point whenever N₁ ≠ N₂. In particular, in the classical Hopf Bifurcation Theorem the numbers N_j are 0 and 1. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)