Wait-and-switch stochastic model of the non-Debye relaxation. Derivation of the Burr survival probability

Stochastic mechanism of relaxation, in which a dipole waits until a favourable condition for reorientation exists, is discussed. Assuming that an imposed direction of a dipole moment may be changed when a migrating defect reaches the dipole, we present a mathematically rigorous scheme relating the local random characteristics of a macroscopic system to its effective relaxation behaviour. We derive a relaxation function (the Burr survival probability) that is characterized by the stretched exponential or the power-law behaviour.     

Measurement of Tumor Vascular Damage in Mice with 99m Tc-MIBI Following Photodynamic Therapy

Abstract— The clinical perfusion agent ^99mTc-MIBI was used to monitor changes in tumor vascular perfusion (TVP) induced by Photofrin® (Pll)-mediated photodynamic therapy (PDT). BALB/c mice bearing an EMT-6 tumor on each hind thigh were given an intravenous injection of 1, 2 or 5 mg kg⁻¹ PII. Twenty-four hours later, one tumor was illuminated (600–650 run, 200 mW cm⁻² 400 J cm⁻²) while the other served as a control. At various time intervals after PDT (0, 2 and 24 h) mice received an intravenous injection of ^99mTc-hexakismethoxy(sobutyusonitri-le (MIBI) (0.18 MBq g⁻¹) and were sacrificed 2 min later. The light-treated and the untreated tumors were then dissected, the radioactivity was counted and the percentage of the injected dose per gram of tumor (%ID g⁻¹) was calculated as a measure of TVP. We observed that TVP is drug dose dependent, develops progressively with time post-PDT and is inversely related to PDT efficacy. Our data show that early tumor retention of ^99mMIBI is a simple method to assess TVP and vascular damage induced by PDT.     

Gas-phase interaction of H2S with O2: A kinetic and quantum chemistry study of the potential energy surface

Quantum chemical calculations were carried out to study the interaction of hydrogen sulfide with molecular oxygen in the gas phase. The basic mechanism, the rates of reaction, and the potential energy surface were calculated. Isomers and transition states that connect the reactants with intermediates and products of reaction were identified using the G2 method and B3LYP/6-311+G(3df,2p) functional. Hydrogen abstraction to form HO2 + SH is the dominant product channel and proceeds through a loose transition state well-described at the level of calculation employed. The temperature dependence of the rate coefficient in the range 300-3000 K has been determined on the basis of the ab initio potential energy surface and with variational transition-state theory. The reaction is 169.5 kJ mol(-1) endothermic at 0 K with a rate constant given by 2.77 x 10(5) T(2.76) exp(-19 222/T) cm3 mol(-1) s(-1) and should proceed slowly under atmospheric thermal conditions, but it offers a route to the initiation of H2S combustion at relatively low temperatures.     

Thermally Induced Carbohydroxylation of Styrenes with Aryldiazonium Salts

The radical carbohydroxylation of styrenes with aryldiazonium salts has been achieved under mild thermal conditions. A broad range of aryldiazonium salts was tolerated, and the reaction principle based on a radical–polar crossover mechanism could be extended to carboetherification as well as to a two‐step, metal‐free variant of the Meerwein arylation leading to stilbenes.     

New semifields, PN and APN functions

We describe a method of proving that certain functions ${f:F\longrightarrow F}$ defined on a finite field F are either PN-functions (in odd characteristic) or APN-functions (in characteristic 2). This method is illustrated by giving short proofs of the APN-respectively the PN-property for various families of functions. The main new contribution is the construction of a family of PN-functions and their corresponding commutative semifields of dimension 4s in arbitrary odd characteristic. It is shown that a subfamily of order p ^4s for odd s > 1 is not isotopic to previously known examples.     

Generalized Einstein conditions on holomorphic Riemannian manifolds

Summary At first, a necessary and sufficient condition for a K?hler-Norden manifold to be holomorphic Einstein is found. Next, it is shown that the so-called (real) generalized Einstein conditions for K?hler-Norden manifolds are not essential since the scalarcurvature of such manifolds is constant. In this context, we study generalized holomorphic Einstein conditions. Using the one-to-one correspondence between K?hler-Norden structures and holomorphic Riemannian metrics, we establish necessary and sufficient conditions for K?hler-Norden manifolds to satisfy the generalized holomorphic Einstein conditions. And a class of new examples of such manifolds is presented. Finally, in virtue of the obtained results, we mention that Theorems 1 and 2 of H. Kim and J. Kim [10] are not true in general.     

Some highly symmetric authentication perpendicular arrays

A set S of permutations of k objects is -uniform, t-homogeneous if for every pair A, B of t-subsets of the ground set, there are exactly permutations in S mapping A onto B. Arithmetical conditions and symmetries are discussed. We describe the character-theoretic method which is useful if S is contained in a permutation group. A main result is the construction of a 2-uniform, 2-homogeneous set of permutations on 6 objects and of a 3-uniform, 3-homogeneous set of permutations on 9 objects. These are contained in the simple permutation groups PSL ₂(5) and PSL ₂(8), respectively. The result is useful in the framework of theoretical secrecy and authentication (see Stinson 1990, Bierbrauer and Tran 1991).     

Anomalous diffusion approach to dielectric spectroscopy data with independent low- and high-frequency exponents

We advance a perspective outcome of tempered α-stable processes used in modeling of anomalous diffusion, a physical mechanism underlying the non-Debye relaxations. The tempered processes are characterized by a heavy tail truncation in time and have finite moments, but they also save some useful features of a purely skewed α-stable process. Due to these features, the relaxation phenomena get a transient character being shown in their asymptotic behavior. From the stochastic subordination scenario of the tempered anomalous diffusion we derive relaxation functions with independent low- and high-frequency exponents falling in the range (0, 1]. Those functions can be used to model all types of experimentally observed two-power-law relaxation patterns.