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Performance based seismic engineering is the modern approach of earthquake resistant engineering. It is an attempt to predict buildings with predictable seismic performance. Therefore, the objectives such as life safety, collapse prevention, or immediate occupancy are used to define the state of the building following a design earthquake. This paper presents the effective computer based seismic performance analysis technique which reduces the tedious calculations and predict exact results. Push over analysis is proposed to estimate the peak responses in load and lateral displacements. The comparison are made in the lower, middle and higher rise structures by using the push over analysis, the performance of the structures can be obtained. Three different structures are taken into consideration for the analysis and their load distributions and lateral displacements are obtained. Those real and only that discourse in this paper will make committed will considerations connected with giving pliability for parts also structures. The discourse in this paper wills a chance to be restricted will monolithically throw reinforced-concrete buildings. The ideas from seismic request also limit would presented and more elaborated on.

This work provides an analytical method for determining the time-dependent effective constitutive response of linear viscoelastic composites with particulate microstructures by means of a differential-algebraic system (DAS) of equations. By making use of differential equations instead of difference equations and utilizing, as primary variables, the variances of the field fluctuations instead of the properties of fictitious linear comparison composites, the new formulation is found to be more robust and to alleviate some of the issues associated with earlier incremental approaches. Remarkably, the new formulation can be shown to recover the exact results of the correspondence principle for isotropic incompressible composites subjected to proportional loading, as well as for isotropic compressible composites subjected to purely hydrostatic loading. More generally, the proposed formulation is not exact but still delivers reasonably accurate estimates in most cases. Lastly, a generalization of the DAS formulation is provided for nonlinear viscoelastic composites with incompressible phases and also found to be more robust than earlier approaches.

A quantum motion of a particle along the x -direction constrained at y = 0 in presence of the Dirac δ -potential is considered. The Green’s function approach is applied for solving the corresponding two-dimensional Schrodinger equation. The exact results for the Green’s function are presented in terms of the Fox H -function, and a generalized integral operator which contains the Mittag-Leffler function in the kernel.

Let F be a family of subsets of { 1 , 2 , … , n } , satisfying | F 1 ∩ F 2 ∩ F 3 | ≥ 4 for all F 1 , F 2 , F 3 ∈ F . It is shown that | F | ≤ 2 n − 4 must hold. This best possible bound was conjectured by the author more than 40 years ago. For the proof several related best possible results are proved for one or several families.

In this work we apply the transfer matrix method to obtain exact solutions for a rod-like interacting unidimensional system and carry out entropic simulations to obtain the same results. A joint density of states is adopted, such that it depends not only of the energy, but also of the total number of dimers and the number of interactions between interacting dimers. We estimate the density of dimers and vacancies, along with the number of interacting links per site, and compare with the exact results. The concordance is excellent.

For a positive integer n , a graph F and a bipartite graph G ⊆ K n , n let F ( n + n , G ) denote the number of copies of F in G , and let F ( n + n , m ) denote the minimum number of copies of F in all graphs G ⊆ K n , n with m edges. The study of such a function is the subject of theorems of supersaturated graphs and closely related to the Sidorenko–Erdős–Simonovits conjecture as well. In the present paper we investigate the case when F = K 2 , t and in particular the quadrilateral graph case. For F = C 4 , we obtain exact results if m and the corresponding Zarankiewicz number differ by at most n , by a finite geometric construction of almost difference sets. F = K 2 , t if m and the corresponding Zarankiewicz number differ by c ⋅ n n we prove asymptotically sharp results based on a finite field construction. We also study stability questions and point out the connections to covering and packing block designs.

Yelp is a platform that provides free access to use the data for educational and research purposes. The sentiment data which is used for this empirical research consists of two attributes namely sentiment text and sentiment count. The sentiment text contains the sentences and the sentiment counts contain their binary sentiment polarity as 0 and 1. 1 means the sentence is positive and 0 means negative. After performing clustering through various approaches like k-means, canopy, cobweb, etc. it is found that none of the approaches gave the exact results. Through this empirical research, we are putting forward the most appropriate approach among various approaches which gave better results for Yelp’s sentiment data and similar types of data. This research is concluded by recommending the clustering approach which is having less error rate and execution time as compared to others.

In this paper, by considering a biased random walker hopping on a one-dimensional lattice with a ring geometry, we investigate the fluctuations of the speed of the random walker. We assume that the lattice is heterogeneous i.e. the hopping rate of the random walker between the first and the last lattice sites is different from the hopping rate of the random walker between the other links of the lattice. Assuming that the average speed of the random walker in the steady-state is v ∗ , we have been able to find the unconditional effective dynamics of the random walker where the absolute value of the average speed of the random walker is − v ∗ . Using a perturbative method in the large system-size limit, we have also been able to show that the effective hopping rates of the random walker near the defective link are highly site-dependent.

The maximum entropy states of the cellular automata models for traffic flow in a single-lane with no anticipation are presented and discussed. The exact analytical solutions for the low-density behavior of the stochastic Fukui–Ishibashi traffic model were obtained and compared with computer simulations of the model. An excellent agreement was found.

Time dependent Dirac delta potential is an interesting problem in quantum mechanics due to its applications in various fields. In this paper we have worked on this problem for two different models. We have derived the propagator for scattering problems in presence of a Dirac delta potential. Here strength of the potential is a function of time i.e. f ( t ) . We have devised a mathematical method to solve this problem using Green's function method. We have also solved the corresponding two state model and find exact results. Our results are purely analytical and we have reported exact expressions of ψ ( x ′ , t ) in all cases.

In this work we consider fixation of an allele in a population. Fixation is key to understanding the way long-term evolutionary change occurs at the gene and molecular levels. Two basic aspects of fixation are: (i) the chance it occurs and (ii) the way the gene frequency progresses to fixation. We present exact results for both aspects of fixation for the Wright-Fisher model. We give the exact fixation probability for some different schemes of frequency-dependent selection. We also give the corresponding exact stochastic difference equation that generates frequency trajectories which ultimately fix. Exactness of the results means selection need not be weak. There are possible applications of this work to data analysis, modelling, and tests of approximations. The methodology employed illustrates that knowledge of the fixation probability, for all initial frequencies, fully characterises the dynamics of the Wright-Fisher model. The stochastic equations for fixing trajectories allow insight into the way fixation occurs. They provide the alternative picture that fixation is driven by the injection of one carrier of the fixing allele into the population each generation. The stochastic equations allow explicit calculation of some properties of fixing trajectories and their efficient simulation. The results are illustrated and tested with simulations.

In the paper the method of numerical homogenization for FGM was proposed It was based on the method shown in Vemaganti and Deshmukh (2006), in which the gradient heterogeneous microstructure is divided into homogenous slices. In the presented study the model was built with the use of 2D elements, with two linear material models of Young modulus E=45 MPa and 748 MPa distributed in sample volume in accordance to linear and normal distributions. Firstly the RVE was calculated. Then the numerical homogenization was carried out with the division of the heterogeneous sample into 4, 5 and 8 slices. The substitute material characteristics were calculated and implemented into sliced model. The numerical compression tests of the sliced and heterogeneous models and were compared. The conclusion was that the more slices we apply the more exact results we will get. This selection should be based on the accuracy we want to get and on the computational capacity we have. Also in this kind of modeling we cannot asses the stress distribution in microstructure.

Utilizing of CFRP for confining concrete columns has been demonstrated to improve the capacity and ductility of columns. In reason of numerous parameters that affect the compressive strength of the CFRP confined rectangular concrete columns (CRCC), developing formula is complicated. In the current study, three methods are evaluated for predicting the residual compressive strength of CFRP CRCC. Multiple regressions (MR), stepwise regression (SR), and artificial neural network (ANN) models were extended as credible methods for generating and evaluating the compressive strength of CFRP CRCC. The required data for training algorithms obtained from a reliable database. The accuracy of the developed formulae is verified using appropriate criteria. Then, a comparison was made between proposed formulae-based models to examine the accuracy degree of these methods. It is understood that despite a negligible difference between proposed models results the obtained formulae based on the SR and ANN methods give the exact results than the MR model.

We define the time-continuous spin coherent-state path integral in a way that is free from inconsistencies. The proposed definition is used to reproduce known exact results. Such a formalism opens new possibilities for applying approximations with improved accuracy and can be proven useful in a great variety of problems where spin Hamiltonians are used.

The first order wetting transition with two defect lines, one near a wall and another at a distance N 1 , in the d = 2 Ising model is studied by the bond propagation algorithm. The numerical calculations are carried out on very large lattices with size up to 160 2 × 160 . The finite size effects of the first order transition in that model are discussed. The magnetization profile is also calculated. The numerical results agree with the exact results very well.

We have obtained the exact expressions for the thermoelectric power and the Lorenz number for the infinite U Hubbard model using orthofermion approach. It is found that in one dimension, our results coincide with that of known exact results. In limiting cases, our exact expressions reduce to the known exact results at low and high temperature limits. We present our calculations for one and two dimensions for square as well as triangular lattices. A comparison between the thermoelectric power and Lorenz number for a free Fermi gas and noninteracting orthofermions has also been provided.

We prescribe analytical expressions for far-field pattern of mono-mode graded index fibers in the low V region. Our formulation is based on the power series expression for fundamental mode of such fibers. The concerned evaluations involve little computations. Taking step and parabolic index fibers as typical examples, we show that the results found by our simple formalism agree excellently with the available exact results. This simple formalism can also be employed to estimate accurately different propagation parameters associated with far-field of such fibers. This accurate but user friendly method will benefit the designers and packagers in the field of optical engineering.

We calculate persistent current of one-dimensional rings of fermions neglecting the spin degrees of freedom considering only nearest-neighbor Coulomb interactions with different electron fillings in both ordered and disordered cases. We treat the interaction exactly and find eigenenergies by exact diagonalization of many-body Hamiltonian and compute persistent current by numerical derivative method. We also determine Drude weight to estimate the conducting nature of the system. From our numerical results, we obtain a metal-insulator transition in half-filled case with increasing correlation strength U but away from half-filling no such transition is observed even for large U., Comment: 5 pages, 9 figures (Accepted for Publication in: Physics Letters A)

We derive exact results for the dynamics of Rouse model in crowded environment modeled by stochastically varying diffusivity, the concept of “diffusing diffusivity”. We specifically generalize the initial analytical formulation of this concept of diffusivity in single particle diffusion to many particle systems with localized interactions, particularly to chains of connected beads, the Rouse model. Independent Rouse modes are allowed to diffuse with stochastically varying time dependent diffusivities to model diffusion in the crowded rearranging environment, where zeroth mode represents the chain center of mass coordinate. We develop an analytical formalism to calculate the probability distribution of these individual mode displacements and subsequently average bead displacement distribution of the Rouse chain and its moments in terms of these modes. The resulting diffusion behavior of thus modified Rouse model is a function of mode resolved parameters which model local interactions and crowded environment collectively. Our analytically tractable implementation of the “diffusing diffusivity” concept to Rouse model is one of its kind that yields non-Gaussian diffusion with the scope of being anomalous and plausibly applied to dynamics in polymeric liquids.

In applications like computer aided design, geometric models are often represented numerically as polynomial splines or NURBS, even when they originate from primitive geometry. For purposes such as redesign and isogeometric analysis, it is of interest to extract information about the underlying geometry through reverse engineering. In this work we develop a novel method to determine these primitive shapes by combining clustering analysis with approximate implicitization. The proposed method is automatic and can recover algebraic hypersurfaces of any degree in any dimension. In exact arithmetic, the algorithm returns exact results. All the required parameters, such as the implicit degree of the patches and the number of clusters of the model, are inferred using numerical approaches in order to obtain an algorithm that requires as little manual input as possible. The effectiveness, efficiency and robustness of the method are shown both in a theoretical analysis and in numerical examples implemented in Python.

If l : V ( G ) → N is a vertex labeling of a graph G = ( V ( G ) , E ( G ) ) , then the d-lucky sum of a vertex u ∈ V(G) is d l ( u ) = d G ( u ) + ∑ v ∈ N ( u ) l ( v ) . The labeling l is a d-lucky labeling if dl(u) ≠ dl(v) for every uv ∈ E(G). The d-lucky number ηdl(G) of G is the least positive integer k such that G has a d-lucky labeling V(G) → [k]. A general lower bound on the d-lucky number of a graph in terms of its clique number and related degree invariants is proved. The bound is sharp as demonstrated with an infinite family of corona graphs. The d-lucky number is also determined for the so-called Gm,n-web graphs and graphs obtained by attaching the same number of pendant vertices to the vertices of a generalized cocktail-party graph.

We study the Biroli-Mezard model for lattice glasses on a number of hierarchical networks. These networks combine certain lattice-like features with a recursive structure that makes them suitable for exact renormalization group studies and provide an alternative to the mean-field approach. In our numerical simulations here, we first explore their equilibrium properties with the Wang-Landau algorithm. Then, we investigate their dynamical behavior using a grand-canonical annealing algorithm. We find that the dynamics readily falls out of equilibrium and jams in many of our networks with certain constraints on the neighborhood occupation imposed by the Biroli-Mezard model, even in cases where exact results indicate that no ideal glass transition exists. But while we find that time-scales for the jams diverge, our simulations cannot ascertain such a divergence for a packing fraction distinctly above random close packing. In cases where we allow hopping in our dynamical simulations, the jams on these networks generally disappear., 9 pages, several corrections. For related information, see http://www.physics.emory.edu/faculty/boettcher/

The first calculation of kaonic deuterium $1s$ level shift using Faddeev-type equations was performed. The obtained results were compared with commonly used approximate approaches., Comment: The version accepted in Phys. Lett. B

The dynamics of the anisotropic Kondo model under the periodic driving is studied. The periodic driving we consider is the local magnetic field which couples with the impurity spin and the in-plane exchange interaction. At the special point in the parameter space (Toulouse limit), the anisotropic Kondo model can be transformed to the non-interacting resonant level model and thereby the exact results for arbitrary external fields can be obtained. It is shown that characteristic behavior of the dynamics changes with the field intensity, the field frequency, and the Kondo temperature. When the local magnetic field intensity is very large compared with the field frequency and the Kondo temperature, the time dependence of the impurity spin and the spin density of the fermionic bath shows an oscillation whose period is inversely proportional to the field intensity. We also find that another time scale, which is given by the inverse of the Kondo temperature, governs the response of the system to the external field.

Evaluating the effectiveness and integrity of forest-based emissions reduction schemes requires appropriate monitoring and evaluation. In order to develop one such approach, this study estimates total carbon stock and change in that stock over time, in REDD+ pilot projects in Nepal, including a comparison of outcomes by different (dominant vegetation and density) forest types. As expected, average biomass carbon was greater in dense canopy forests than sparse ones in all vegetation types. More particularly, carbon stock was highest in dense canopy of Shorea robusta forests followed by mixed broad-leaf forests, Rhododendron-Quercus forests, Pine forests and Schima–Castanopsis forests. On average, carbon stock increased in forests under the REDD+ activities during the study period (2010–13). The carbon increment between 2010 and 2013 was higher in dense forests with dominant Pine vegetation (24 Mg C/ha) followed by Schima–Castanopsis (20 Mg C/ha), mixed broad leaf types (18.9 Mg C/ha) and S. robusta (16.9 Mg C/ha), while the lowest was found in sparse canopy of Rhododendron-Quercus vegetation (5.9 Mg C/ha). The results suggest that funding agencies could maximise carbon stock by targeting particular forest types, but it should be noted that this has implications for the conservation and management practices for, and income from, community forests. The results of this study will be useful in designing REDD+ policies and programmes in Nepal. Although the exact results of the study could not be applicable; the approach, framework of the study and knowledge can be applied in several other developing countries with similar community-based forest management systems

A novel shooting method with excellent simple control strategy is developed for solving the failure to convergence of the traditional shooting methods themselves in fiber lasers model. Compared with the published literature, the novel shooting method provides a clear physical understanding method for getting the threshold pump power and the exact results with given random functions in Yb3+-doped fiber lasers and Er3+-doped fiber lasers. Then, the results in Er3+-doped fiber lasers and Yb3+-doped fiber lasers demonstrate that the solutions using the novel shooting method has high accuracy of 10−8 W with several iteration steps, which have extended the applicable range of the end-pumped power even lower than 1 mW pump power. Furthermore, compared with 1480 nm pump for the threshold and slope efficiencies of the Er3+-doped fiber lasers, 978 nm fiber lasers can extend wider scope of application and be pump source in the coming future. Finally, the lower threshold and higher slope efficiency at 975 nm than those of 910 nm pump in Yb3+-doped fiber lasers, 975 nm pump laser provides for broad band excellent cladding pump source.

The effective-field theory is used to study the anomalous metamagnetic behavior of a uniaxial ferromagnetic film, which has been observed in the recent experiment Riego et al. (2017). Similar to experimental findings, the sidebands phenomena of the dynamic susceptibility have been shown in certain ranges of the bias field, as well as the amplitude and period of the oscillating magnetic field. The mechanism and precise nature of the anomalous metamagnetic behavior have been explored in detail as well. We also compare the effective-field theory results to those produced using mean-field theory and Monte Carlo simulations. We find that the analytic treatment of the effective-field theory is in good qualitative agreement with exact results of the Monte Carlo simulations.

The paper addresses the development of Lattice Boltzmann (LB) methods for turbulent flows in response to a recent paper of Tan et al. [1] . Exact results, which ensure the consistency of LB equations with turbulence transport equations, are presented for parameters in LB equations. The advantages of using the exact LB model parameter setting are pointed out.

We give exact results for the polarizabilities, longitudinal and transverse, of two parallel cylinders of the same radius. The expressions are infinite sums, which converge rapidly if the cylinders are separated by a radius or more. In close approach the sums converge slowly, but are replaced by equivalent integral expressions, which give simple analytical results in this limit. The contact values of the longitudinal and transverse polarizabilities are π 2 /6 and π 2 /12 times the large-separation values. The longitudinal contact value is approached infinitely rapidly as the separation tends to zero, while the approach of the transverse polarizability to its contact value is regular.

The polarization switching properties of ferroelectric materials have been extensively studied, both experimentally and theoretically owing to their wide applications in industry and hence generating a need to gain a deeper understanding of factors affecting their switching behaviour. In this paper, an analytical Landau theory incorporating the Landau–Khalatnikov equation has been developed to describe the switching properties of second order ferroelectrics. Analytical expressions derived from exact results of Landau theory are used in modelling work carried out in this study for comparison with trends predicted by empirical laws used to describe polarization switching behaviour at high electric fields. As such this work has established the theoretical basis for empirical laws of polarization switching and developed simple numerical tools which can be quickly used to model trends in polarization switching behaviour of ferroelectrics.

We report an exact, analytical solution to the problem of a hollow sphere subjected to hydrostatic tension and made of ideal-plastic porous material, obeying a micromorphic model developed by Gologanu, Leblond, Perrin and Devaux (GLPD). The motivation is to find analytical solutions for simple problems that might be of interest to assess the robustness of the numerical implementation of the micromorphic model into finite element codes. We provide the details of the analytical calculations of the deformation, stress and moment distributions. We demonstrate the validity of our analytical results by comparing them to the solution of the classical problem of a hollow sphere whose matrix obeys the von Mises model, subjected to hydrostatic tension.

Obtaining exact results for larger problem instances of the intractable problems is still an important issue. Genetic algorithms can provide good solutions for such problems by using appropriate recombination and mutation operators to search the solution space, provided that they are given a sufficient population size of individuals and enough time to iterate through generations. There are numerous proposed recombination operators that programmers use for this purpose. Most of the time, one of these operators are randomly selected to solve a problem without knowing its capabilities. In this study, we analyze the most used recombination operators and propose a new swap-based operator, Bubble Recombination Operator (BRX), for the intractable permutation problems. The proposed operator swaps iteratively and outperforms most of the well-known permutation recombination operators. BRX provides either the optimum or very close to the best available solutions reported so far for the problem instances of the Quadratic Assignment Problem.

Correlation functions play an important role in determining the structural and energetic properties of electronic systems. However, exact results are available only for ideal systems free of electrostatic interactions. Here we present a liquid-state method that combines classical mapping of the Pauli exclusion principle with the universality ansatz of the bridge functional. We show excellent agreement of the new method with quantum Monte Carlo simulation for predicting the electronic correlation functions and thermodynamic properties of uniform electron systems.

Magnetocaloric properties of the two-leg frustrated spin ladder system are investigated by the use of transfer-matrix method. Exact results for the magnetization, entropy, entropy change and magnetocaloric cooling rate versus temperature and field are presented and discussed in detail. Large inverse magnetocaloric effects induced by the field arise at low temperature, and exhibit strong dependency relationship on the exchange couplings. In the vicinity of the critical field, the enhanced inverse magnetocaloric effects and normal magnetocaloric effects are both observed. Besides, the influences of the single-ion anisotropy on the entropy change are discussed as well.

Calculation of bend loss for single-mode graded-index fibers utilizes the fundamental modal field. Using some of the single and two parameter scalar variational approximations available in the literature for this mode, the bend loss has been computed. The exact results are obtained using a well known numerical method. The accuracies of the results obtained from the use of these variational fields have been compared.

We analytically address the non-equilibrium problem of a Brownian particle in contact with a thermal reservoir by means of a non-Gaussian Langevin noise term η ( t ) . The presence of noise kurtosis is akin to a second temperature reservoir acting on the system, and we exploit its consequences by means of studying a converging exact form for the stationary probability distribution.

The exact evaluation of the disconnected diagram contributions to the flavor-singlet pseudo-scalar meson mass, the nucleon σ-term and the nucleon electromagnetic form factors is carried out utilizing GPGPU technology with the NVIDIA CUDA platform. The disconnected loops are also computed using stochastic methods with several noise reduction techniques. Various dilution schemes as well as the truncated solver method are studied. We make a comparison of these stochastic techniques to the exact results and show that the number of noise vectors depends on the operator insertion in the fermion loop. © 2012 Elsevier B.V. All rights reserved. 183 6 1215 1224 Cited By :16

The recurrence properties of random walks can be characterized by Polya number, i.e. , the probability that the walker has returned to the origin at least once. In this paper, we investigate Polya number and first return for bursty random walk on a line, in which the walk has different step size and moving probabilities. Using the concept of the Catalan number, we obtain exact results for first return probability, the average first return time and Polya number for the first time. We show that Polya number displays two different functional behavior when the walk deviates from the recurrent point. By utilizing the Lagrange inversion formula, we interpret our findings by transferring Polya number to the closed-form solutions of an inverse function. We also calculate Polya number using another approach, which corroborates our results and conclusions. Finally, we consider the recurrence properties and Polya number of two variations of the bursty random walk model.

It is known that a circular shaft containing a number of composite cylinders, upon suitably designed material parameters, is an exactly solvable configuration under Saint-Venant’s torsion [Chen, T., Benveniste, Y., & Chuang, P. C. (2002). Exact solutions in torsion of composite bars: Thickly coated neutral inhomogeneities and composite cylinder assemblages. Proceedings of the Royal Society A, 458, 1719–1759]. Here we consider the boundary value problem of a circular shaft containing coated fibers under torsion without any restrictions on the material parameters. The formulation is based on a complex variable method together with simple mapping techniques, representing the warping fields in Laurent or Taylor series based on different origin points. Particularly when the coated fibers are periodically dispersed inside the host shaft, we show that the unknown coefficients for each coated fiber are correlated in specific manners, and thus rendering the governing framework much simplified. We verify analytically that our results conform with the exact results of partly neutrality and complete neutrality of the exact solvable configuration of a circular shaft containing neutral coated fibers. This work presents a feasible solution procedure that complements the exact configurations in which the material parameters must follow restrictive constraint, and also provides an estimate for the torsional rigidity in which the bounds are not sufficiently close.

A novel technique for treating electrically thin dispersive layers with the finite-difference time-domain (FDTD) method based on Z transforms is introduced. The proposed model is based on the subcell technique, where the constitutive relations are locally averaged in the FDTD grid. The most significant feature of the proposed model is its ability to model rather complicated dispersive layers having multiple pole pairs. Then, based on the model above, the model for pulse reflection from a coated ideal conductor is proposed. The models are validated with several numerical examples making comparison with the exact results.

The paper deals with the stationary problems of diffusion in a homogeneous isotropic layer with a cylindrical hole. The hole is partially filled by diffusing substance. The considered problem is described within the framework of the Fick's law and the integral Weber–Orr transform method is applied to solve it. The obtained exact results expressed by integrals will be presented in the form of figures.

In order to provide some basic evaluations of elementary nodal techniques, as used in the general area of particle transport theory, critical and albedo problems for cylinders, spheres, and slabs are solved approximately in terms of averaged quantities and compared to exact results.

We introduce simple practical approximations for various diffusion-influenced reactions in two dimensions, which are found to be superior to previously known approximations at long times. The approximations for the irreversible reactions with the Smoluchowski boundary condition are found to be in excellent agreement with the numerically exact results at all times. We generalize the long-time approximations to be applied to more complicated geminate diffusion–reaction systems such as the excited-state reversible binding and transfer reactions.

In this paper a formalism, called perturbational crystal orbital theory, is proposed and examined. This formalism is based on a recent formulation of the perturbational molecular orbital theory in matrix form, and could be considered as an extension of it to periodic lattices. The perturbational crystal orbital theory is applied to the study of the energy band changes due to geometrical and electronegative perturbations of a 1D lattice. For these cases, the exact results are compared with those obtained by applying the proposed formalism up to second order, and a discussion of those results is carried out.

For an integer k ? 1 , the k -improper upper chromatic number ? ? k - imp ( G ) of a graph G is introduced here as the maximum number of colors permitted to color the vertices of G such that, for any vertex v in G , at most k vertices in the neighborhood N ( v ) of v receive colors different from that of v . The exact value of ? ? k - imp is determined for several types of graphs, and general estimates are given in terms of various graph invariants, e.g.?minimum and maximum degree, vertex covering number, domination number and neighborhood number. Along with bounds on ? ? k - imp for Cartesian products of graphs, exact results are found for hypercubes. Also, the analogue of the Nordhaus-Gaddum theorem is proved. Moreover, the algorithmic complexity of determining ? ? k - imp is studied, and structural correspondence between k -improper C-colorings and certain kinds of edge cuts is shown.

Exact results are given for the forces per unit length acting on each of a pair of parallel conducting cylinders when polarized by an external electric field perpendicular to the cylinders. Simple analytic results are obtained at small and large separations of the cylinders. The torque on the cylinders (which acts to align them with the electric field) is proportional to the difference between the longitudinal and transverse polarizabilities. The forces acting on the cylinders (which are equal and opposite) are given by the derivatives of the polarizabilities with respect to their separation.

This paper develops a continuous-time model for valuing executive stock options (ESOs) with features of early exercise, delayed vesting and forfeiture. Applying the quadratic approximation established for valuing American options into ESOs, we obtain an explicit formula for the fair ESO value at its grant date. We show that the approximation formula is consistent with the exact results for two special cases either with no dividend or infinite maturity, and also that the perpetual value for the latter case gives an upper bound of the ESO value. To see the performance of the formula, we numerically examine it with benchmark results generated by a binomial-tree model for some particular cases. Numerical experiments show that there is a complementary relation between the vesting and trading periods with respect to exit rate of ESO holders.

This paper used an ideal periodic solution which is called max–min approach (MMA) to evaluate oscillation systems with nonlinearity terms such as motion of a rigid rod rocking back. This method introduces an alternative to overcome the difficulty of computing the periodic behavior of the oscillation problems in engineering. To assess the accuracy of solutions, the results were compared with the exact ones. The most significant features of this method are the simplicity and the excellent agreement with the exact results for the various parameters. Furthermore, the results reveal that one iteration leads to high accuracy of the solution. This solution may be useful for the explanation of some practical physical problems.

Regulation of mRNA decay is a critical component of global cellular adaptation to changing environments. The corresponding changes in mRNA lifetimes can be coordinated with changes in mRNA transcription rates to fine-tune gene expression. Current approaches for measuring mRNA lifetimes can give rise to secondary effects due to transcription inhibition and require separate experiments to estimate changes in mRNA transcription rates. Here, we propose an approach for simultaneous determination of changes in mRNA transcription rate and lifetime using regulatory small RNAs (sRNAs) to control mRNA decay. We analyze a stochastic model for coupled degradation of mRNAs and sRNAs and derive exact results connecting RNA lifetimes and transcription rates to mean abundances. The results obtained are then generalized to include nonstoichiometric coupled degradation of sRNAs. Our analysis suggests experimental protocols for determining parameters controlling the efficiency of stoichiometric regulation by small RNAs and for analyzing factors and processes regulating changes in mRNA transcription and decay.

We investigate different treatments of continuum states in a simple structure case: two particles moving in a one-dimensional mean field and interacting via a density-dependent short range residual interaction. We find that in procedures that involve continuum discretization a rather large basis has to be used in order to get convergence to the exact results, in particular for the radial dependence of the two-particle wave function. This may lead to unpracticable situations in the case of many interacting particles in the continuum.