Study of an identity

We solve the word problem of the identity x(yz) = (xy)(yz) by investigating a certain group describing the geometry of that identity. We also construct a concrete realization of the one-generated free algebra relative to the above identity. Received March 23, 2001; accepted in final form July 6, 2002.     

Differential Pulse Polarographic Determination of Nitrate in AUT Solution

A differential pulse polarographic method for the determination of nitrate ion has been developed. With 0.5 M CaCl₂ as supporting electrolyte, NO^?₃ is reduced to give a peak with E_1/2=–1.836 Volt vs. the Ag/AgCl electrode. The differential pulse polarographic peak height is proportional to the nitrate concentration from 20 to 60 ppm. The detection limit for nitrate is 2 ppm in pure aqueous solution. In the determination of 40 ppm nitrate a relative precision (relative standard deviation) of less than 2% was achieved. Nitrite interferes seriously and should be absent if accurate results are required. The method has been applied to the determination of nitrate in Ammonium Uranyl Tricarbonate (AUT) Solution, results obtained by this method are compared to those obtained by ion chromatography. The agreement between the two sets of results suggests that the DPP method can be used with a fair degree of confidence.     

Enhancement in age hardenability of sintered Ti–5Fe alloy by Zr addition processed by pulsed electric current sintering

The age-hardenable Ti–5Fe–5Zr (wt. %, 5Zr) alloy has been consolidated by pulsed electric current sintering, following a β solution treatment, and the results are compared with a Ti–5Fe (0Zr) alloy. The precipitation sequence measured at 640°C ageing is β?+?athermal ω?→?β?+?isothermal ω?→?β?+?α. At the peak hardness isothermal ω phase forms at 20?s of ageing. The Zr addition retards the precipitation kinetics of the α phase; as a result, the α phase nucleates at latest at 300?s ageing in the overaged state. Fe is partitioned into β, while it is depleted from the α phases. There is Zr enrichment near the α/β interface when the α phase precipitates due to a solute drag effect; the growth rate of the α phase in the 5Zr alloy is significantly reduced compared with that in the 0Zr alloy.     

字定理在Heegaard分解方面的一个应用

The word theorem states that x can be denoted as a rotation inserting word of A if x is in the normal closure of A in F(X). As an application of the theorem, in this note a condition that guarantees reducing the genus of Heegaard splitting of 3-manifolds is given. This leads Poincare conjecture to a new formulation.     

2IV^m-p设计的弱最小低阶混杂与纯净效应准则等价的条件

该文给出了2IVm-p设计包含最多纯净两因子交互效应与该设计具有弱最小低阶混杂等价的几个条件．并在文章的末尾给出了一组既具有弱最小低阶混杂又包含最多纯净两因子交互效应的2IVm-p设计．     

On the complexity of the word problem for automaton semigroups and automaton groups

In this paper, we study the word problem for automaton semigroups and automaton groups from a complexity point of view. As an intermediate concept between automaton semigroups and automaton groups, we introduce automaton-inverse semigroups, which are generated by partial, yet invertible automata. We show that there is an automaton-inverse semigroup and, thus, an automaton semigroup with a PSpace-complete word problem. We also show that there is an automaton group for which the word problem with a single rational constraint is PSpace-complete. Additionally, we provide simpler constructions for the uniform word problems of these classes. For the uniform word problem for automaton groups (without rational constraints), we show NL-hardness. Finally, we investigate a question asked by Cain about a better upper bound for the length of a word on which two distinct elements of an automaton semigroup must act differently.A detailed listing of the contributions of this paper can be found at the end of this paper.     

The next step of the word problem over monoids

It is known that a group presentation P can be regarded as a 2-complex with a single 0-cell. Thus we can consider a 3-complex with a single 0-cell which is known as a 3-presentation. Similarly, we can also consider 3-presentations for monoids. In this paper, by using spherical monoid pictures, we show that there exists a finite 3-monoid-presentation which has unsolvable “generalized identity problem” that can be thought as the next step (or one-dimension higher) of the word problem for monoids. We note that the method used in this paper has chemical and physical applications.     

On Word Equations Originated from Discrete Dynamical Systems Related to Antisymmetric Cubic Maps with Some Applications

In this article, we solve some word equations originated from discrete dynamical systems related to antisymmetric cubic map. These equations emerge when we work with primitive and greatest words. In particular, we characterize all the cases for which <β₁β₁>=<β₂β₂> where β₁ and β₂ are the greatest words in <<β₁>> and <<β₂>> of M(n).     

Manipulation of light at the nanoscale for high-performance spectroscopic and optical applications

In this paper, we explore the use of nanostructures for a number of fascinating applications. These applications based on nanostructures include (1) optical sensors, (2) nanopixel printing, (3) improving the resolution of imaging techniques, and (4) lithography. In the sensing field, nanostructures are exploited for advanced sensor performance, namely, the label-free and enhanced sensitivity of (1) the surface plasmon resonance sensor and (2) the extraordinary optical transmission sensor and (3) the high sensitivity and selectivity of surface-enhanced Raman spectroscopy. In addition, research using nanostructures for visual applications was introduced for (1) harnessing nanostructures for full-color pixel printing and (2) exploiting metallic nanostructures to enhance the imaging resolution under diffraction limits based on the plasmonic effect. Finally, we introduce low cost, high accuracy, and fast lithographic methods based on the plasmonic effect by exploiting metallic nanostructures.     

Comprehensive study on hot carrier reliability of radiation hardened H-gate PD SOI NMOSFET after gamma radiation

ABSTRACT

The authors perform gamma ray irradiation and hot carrier stress on RH H-Gate PD (partially depleted) SOI NMOSFETs as the experimental group and commercial strip-shaped gate PD SOI NMOSFETs as the control group. They analyse HCI degradation in samples and conclude that radiation could enhance HCI degradation in RH H-gate samples. Moreover, the mechanism is explained as the coupling effect between the front gate and back gate caused by TID radiation-induced trap charges in the buried oxide.