Uniform convergence and integrability of Fourier integrals

Firstly, we study the uniform convergence of cosine and sine Fourier transforms. Secondly, we obtain Pitt-Boas type results on Lp-integrability of Fourier transforms with the power weights. The solutions of both problems are written as criteria in terms of general monotone functions.     

Least squares solution with the minimum-norm to general matrix equations via iteration

Two iterative algorithms are presented in this paper to solve the minimal norm least squares solution to a general linear matrix equations including the well-known Sylvester matrix equation and Lyapunov matrix equation as special cases. The first algorithm is based on the gradient based searching principle and the other one can be viewed as its dual form. Necessary and sufficient conditions for the step sizes in these two algorithms are proposed to guarantee the convergence of the algorithms for arbitrary initial conditions. Sufficient condition that is easy to compute is also given. Moreover, two methods are proposed to choose the optimal step sizes such that the convergence speeds of the algorithms are maximized. Between these two methods, the first one is to minimize the spectral radius of the iteration matrix and explicit expression for the optimal step size is obtained. The second method is to minimize the square sum of the F-norm of the error matrices produced by the algorithm and it is shown that the optimal step size exits uniquely and lies in an interval. Several numerical examples are given to illustrate the efficiency of the proposed approach.     

A switch-modulated method for chaos digital secure communication based on user-defined protocol

In this paper, a scheme for digital secure communication is proposed. In this scheme, we use a control function which is defined by two communicants based on chaos synchronization. At first, different signals are sent according to the promissory transmission situation of control signal, then transmission field which is consist of protocol and transmission content is produced. After these processing, the correlation of the transmitted signals are decreased. In addition, the using of the compound non-linear function transformation can further intercalate the secret key, so a determined intruder is very difficult to retrieve the message using forecasting method.     

Spinal fMRI investigation of human spinal cord function over a range of innocuous thermal sensory stimuli and study-related emotional influences

Functional magnetic resonance imaging (fMRI) of the human spinal cord has revealed important details of activity involved with innocuous sensory stimuli, including the primary input to ipsilateral dorsal gray matter and activity in bilateral ventral gray matter regions. The latter is hypothesized to reflect descending modulation from the brainstem and cortex. Here, the functions corresponding to these areas of activity are investigated by varying the temperature of innocuous thermal stimuli, and the order they are presented, across repeated fMRI experiments in the spinal cord and brainstem. Group results and connectivity analyses reveal that the ipsilateral dorsal gray matter (dGM), the primary site of sensory input, also receives inhibitory input from the rostral ventromedial medulla and the locus coeruleus, two components of the brainstem opiate analgesia system. Ipsilateral ventral gray matter (vGM) receives input from the ipsilateral dGM and inhibitory input from the pontine reticular formation, which is involved with coordination of movements by modulation of ventral horn cells. Contralateral vGM regions appear to receive input from only the ipsilateral dGM in these studies. These results provide an unprecedented view of details of human spinal cord function and descending modulation, and have important implications for assessment of the effects of spinal cord trauma and disease by means of fMRI.     

Quenching efficiency of “hot" polar molecules by He buffer gas at ultralow energies: quantum results for MgH and LiH rotations

Rotationally superelastic collisions are computed from quantum dynamical calculations for the two title systems, down to the very low collision energies of interest in cold trap experiments. The results are obtained via ab initio interaction potentials, the one for the MgH-He system being given here for the first time and discussed in details in the present paper. The calculations show marked differences in behaviour for both cooling efficiency rates at vanishing temperatures and individual cross sections between levels, and their origin is related to target structural properties and with specific features of the two potentials.     

Squeezed thermal spin states of magnons in the ferromagnet

In this paper, we discuss squeezed thermal spin states of magnons that are described by the Heisenberg Hamiltonian in the ferromagnet, in which the magnon system possesses a new kind of quasiparticle, which we call ferromagnon, i.e. a “dressed” quasi-particle obtained from the magnons by a Bogoliubov-Valatin transformation . Generally, the mass and noise properties of ferromagnons possess potentially important and novel effects in condensed matter physics, which have extensive application in the fields of science and technology. Moreover, it is convenient to introduce the Holstein-Primakoff method, in order to take into account the nonlinear interaction among spin waves. At last we describe the quantum fluctuations of spin-components in the squeezed thermal spin states of magnons and their temperature-dependence. Below some temperature, the squeezed thermal spin states of ferromagnons show squeeze effect.     

Accurate analytical approximate solutions to general strong nonlinear oscillators

A new approach is presented for establishing the analytical approximate solutions to general strong nonlinear conservative single-degree-of-freedom systems. Introducing two odd nonlinear oscillators from the original general nonlinear oscillator and utilizing the analytical approximate solutions to odd nonlinear oscillators proposed by the authors, we construct the analytical approximate solutions to the original general nonlinear oscillator. These analytical approximate solutions are valid for small as well as large oscillation amplitudes. Two examples are presented to illustrate the great accuracy and simplicity of the new approach.     

Electronic structure ofCuNi,CuCo andAgNi alloys

Summary The pseudo Green's function theory for dilute alloys ofd-band metals is used to study the electronic structure ofCuNi,CuCo andAgNi alloys. The calculated densities of state are found in agreement with other available results. The virtual bound states with double-hump structure are found at 0.514, 0.54 and 0.4 Ryd forCuNi,CuCo andAgNi alloys, respectively.

---

Riassunto La teoria della pseudo funzione di Green per leghe diluite di metalli nella bandad è usata per studiare la struttura elettronica delle legheCuNi,CuCo eAgNi. Si trova che le densità di stato calcolate sono in accordo con altri risultati disponibili. Gli stati legati virtuali con struttura a doppia sporgenza si trovano a 0.514, 0.54 e 0.4 Ryd per leghe diCuNi,CuCo eAgNi.

---

Резуме Используется теория псевдо-гриновских функций для разбавленных сплавов металловd-зоны, чтобы исследовать злектронную структуруCuNi,CuCo иAgNi. Получено, что вычисленная плотность состояния согласуется с другими имеющимися результатами. Обнаружены виртуальные связанные состояния, имеюшие структуру с двойным максимумом, при 0.514, 0.54, 0.4 Ry соответственно для сплавовCuNi,CuCo иAgNi.

     

A statistical method for predicting alpha-helical and beta-sheet regions in proteins from their amino acidic sequences

Summary In this paper we propose a new method to predict the secondary structure of proteins from sequence data. A satisfactory improvement of the available efficiency of prediction is obtained. The described method takes into account the frequency of each pair of amino acids in alpha-helical, beta-sheet and random coil regions according to previous results that the sequences of amino acidic residues in these regions are autocorrelated. The rules of the method are not derived from the analysis of the regions of proteins with a known secondary structure, but they are instead based on statistical considerations. In such a way the obtained value of efficiency of the method (88%) has a high reliability: in fact, it is correct to test a method only on the data not used to construct it. A new definition of efficiency of a predictive method is given to resolve the ambiguities arising from the previously accepted definitions.

---

Riassunto In questo lavoro si propone un nuovo algoritmo per predire la struttura secondaria di una proteina dall’analisi della sua sequenza aminoacidica, con il quale si è ottenuto un significativo miglioramento delle efficienze di previsione della struttura secondaria disponibili fino ad ora. Il metodo descritto tiene conto della frequenza delle coppie adiacenti di aminoacidi nelle regioni ad alpha-helix, beta sheet e random coil, in accordo con il nostro precedente risultato che in tali regioni le sequenze aminoacidiche sono autocorrelate. Le regole usate non derivano dall’analisi delle regioni di proteine con una struttura secondaria nota, ma sono invece basate esclusivamente su considerazioni statistiche. In tal modo il valore ottenuto per l’efficienza del metodo (88%) ha un’alta affidabilità, essendo corretto controllare un metodo solo sui dati non utilizzati per la sua costruzione. Per risolvere le ambiguità esistenti, inoltre, si dà qui una nuova definizione di efficienza per un metodo di previsione di strutture secondarie.

---

Резюме В этой работе предлагается новый метод для предсказания вторичной структуры белков, исходя из последовательности аминокислот. Получается существенное улучшение эффективности предсказания. Предложенный метод учитывает частоту каждой пары аминокислот в альфа-спиральной области, бета-слоистой области и в области случайных спиралей, в соответствии с предыдущими результатами, согласно которым последовательности аминокислот в этих областях являются автокоррелированными. Правила метода не выводятся из анализа областей белков с известной вторичной структурой, а основываются на статистических рассмотрениях. Полученное значение эффективности (88%) имеет высокую надежность. Корректность метода проверялась не только на данных, использованных для его конструирования. Предлагается новое определение эффективности для разрешения неоднозначностей, связанных с ранее принятыми определениями.