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As a space-filling method, Voronoi Treemaps are used for showcasing hierarchies. Previously presented algorithms are limited to visualize nonspatial data. The approach of spatial Voronoi Treemaps is proposed in this paper to eliminate these problems by enabling the subdivisions for points, lines, and polygons with spatial coordinates and references. The digital distance transformation is recursively used to generate nested raster Voronoi polygons while the raster to vector conversion is used to create a vector-based Treemap visualization in a GIS (geographic information system) environment. The objective is to establish a spatial data model to better visualize and understand the hierarchies in the geographic field.

Capacity definition recognises that only traverse point or uniform section of roadway capacity can be estimated. Since midblock median U-turn opening is a nonuniform infrastructure, a novel capacity estimation method is needed. The paper proposes sectioning models for estimating U-turn capacity based on dynamics and regression theory. Surveyed U-turn roadway was divided into three sections (entry, middle curve, and exit). Traffic data for each section and adjoining priority traffic stream were collected continually for eight weeks. After modifying passenger car values, ensuing traffic flows and computed densities were used to develop capacity model for entry and middle curve. Regression models where traffic flows from the exit section were taken as the dependent variables and flows from the priority stream were taken as independent variable were used to model capacity for the exit section. Sensitivity analysis shows that the proposed models can produce reliable and accurate results. Results reveal that that traffic capacity at entry (1221 pcu/h) and exit (about 350 pcu/h) sections differs significantly. The paper concluded that U-turn roadway capacity cannot be generalized because the structure is nonuniform.

This paper proposes a new approach for the performance analysis of a single-stage solar adsorption refrigeration system with activated carbon-R134a as working pair. Use of artificial neural network has been proposed to determine the performance parameters of the system, namely, coefficient of performance, specific cooling power, adsorbent bed (thermal compressor) discharge temperature, and solar cooling coefficient of performance. The ANN used in the performance prediction was made in MATLAB (version 7.8) environment using neural network tool box.In this study the temperature, pressure, and solar insolation are used in input layer. The back propagation algorithm with three different variants namely Scaled conjugate gradient, Pola-Ribiere conjugate gradient, and Levenberg-Marquardt (LM) and logistic sigmoid transfer function were used, so that the best approach could be found. After training, it was found that LM algorithm with 9 neurons is most suitable for modeling solar adsorption refrigeration system. The ANN predictions of performance parameters agree well with experimental values with R2 values close to 1 and maximum percentage of error less than 5%. The RMS and covariance values are also found to be within the acceptable limits.

Recorded electroencephalography (EEG) signals can be represented as square matrices, which have been extensively analyzed using mathematical methods to extract invaluable information concerning brain functions in terms of observed electrical potentials; such information is critical for diagnosing brain disorders. Several studies have revealed that certain such square matrices—in particular, those related to so-called “elementary EEG signals”—exhibit properties similar to those of prime numbers in which every square EEG matrix can be regarded as a composite of these signals. A new approach to ordering square matrices is pivotal to extending the idea of square matrices as composite numbers. In this paper, several ordering concepts are investigated and a new technique for ordering matrices is introduced. Finally, some properties of this matrix order are presented, and the potential applications of this technique to analyzing EEG signals are discussed.

The paper on the analysis of data from transduction experiments with Salmonella typhimurium, which was published in Genetical Research (Dawson, 1963), unfortunately contained an error on p. 419. In calculating the limiting values X/Y, the formulae for d and d′ are correctly stated, but their solutions are transposed. The last and third last lines on p. 419 should therefore be interchanged. In the arithmetic example on pp. 420 and 421, a similar interchange of the calculations of d and d′ is necessary. The maximum value of a/b is then:and the calculation of the minimum value should be:These values of 2·20 and 1·23 are to be compared with the values of 2·23 and 1·24 in the published paper.

The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. In this paper, we investigate the concept of restricted positive definite functions and their relation with restricted representations of an inverse semigroup. We also introduce the restricted Fourier and Fourier-Stieltjes algebras of an inverse semigroup and study their relation with the corresponding algebras on the associated groupoid.

In this paper we prove that the fractional derivative or the fractional primitive of a $T$-periodic function cannot be a $\tilde{T}$-periodic function, for any period $\tilde{T}$, with the exception of the zero function., 12 pages

As regulators pay more attentions to losses rather than gains, we are able to derive a new class of risk statistics, named regulator-based risk statistics with scenario analysis in this paper. This new class of risk statistics can be considered as a kind of risk extension of risk statistics introduced by Kou et al. \cite{11}, and also data-based versions of loss-based risk measures introduced by Cont et al. \cite{5} and Sun et al. \cite{12}.

The basic recurrence equations given in our previous paper have to be modified when males and females are differentiated. The modifications we gave are incorrect because we ignored the deviations from Hardy–Weinberg equilibrium when sampling and selection are applied separately to the two sexes. Appropriate corrections are presented in this paper.

SUMMARYIn this paper an exact treatment is given for the stochastic behaviour of the frequency of haploid genotypes in an infinite population when the absolute fitnesses of the two genotypes vary at random over generations. The main qualitative result from this treatment is that natural selection will favour that allele with the largest geometric mean fitness. A diffusion equation is derived whose solution is identical to the exact solution. The drift coefficient for this equation is of the form − μp(1 −p) + σ2(½ −p)p(l −p). This differs from the drift coefficient used in previous treatments of this problem and reduces the rate of quasi-fixation. Various waiting time problems are solved using this diffusion equation.

Assessing the demand hazards of structures is requested in the framework of performance-based earthquake engineering. An efficient method for estimating the seismic risk of structures is proposed in this paper. The relationship between multiple limit capacities and corresponding response parameters is denoted by using a generalized multidimensional limit state equation. The limit states of different components are described as random and convex mixed variables. The seismic responses of different components are considered dependent and follow a multidimensional lognormal distribution. The mathematical formula of multidimensional demand hazards of structures is then derived through combining the seismic fragility function and the seismic hazard curve. The proposed method is used to perform the demand hazard analysis and the parameter sensitivity analysis of a multispan continuous concrete girder bridge, selecting column ductility and bearing displacement as the two-dimensional seismic response parameters obtained by Incremental Dynamic Analysis. The results demonstrate that the coefficient of variation and correlation coefficient N, which are involved in the limit state equation, have an impact on the evaluation of the demand hazards.

The augmented Jacobi polynomials, designated Zℓmn by Roe, or the closely related generalized Legendre functions, Pℓmn(cos⁡ϕ) of Bunge, are required for series expansions of the crystallite orientation distribution. The problem of publishing extensive tabular information has limited compilation of these functions to certain crystal and physical symmetries. This paper gives a brief description and listing of a computer program which permits calculation of Fourier sine (m–n odd) or cosine (m–n even) series expansions of Zℓmn(ξ) for ℓ=0,1,…,32; m=0,1,…,ℓ; n=0,1,…,ℓ.

To compensate for variations in canning practices, canned acid foods are systematically overprocessed to assure commercial sterility. For maximum yield and quality, common processing variables such as fill weight, headspace, consistency of covering medium and vacuum conditions should be standardized and controlled so that overprocessing can be minimized. It was found, for example, that in terms of integrated sterilizing values (I.S.27212), process lethality can decrease 30–40% when tomato fill weights in 303 × 406 cans increase from 7 to 15 oz. Evaluation of fruit condition showed that firm tomatoes can achieve 36% higher lethality than soft tomatoes for the same amount of energy input. Approximately 40 rpm (can) appeared to be most suitable for the flame processing of tomatoes packed in juice into 303 × 406 cans. By operating the commercial flame sterilizer at full capacity, a significant increase in internal can temperature can be achieved.

LetGdenote the dyadic group, which has as its dual group the Walsh(-Paley) functions. In this paper we formulate a condition for functions inL1(G)which implies that their Walsh-Fourier series converges inL1(G)-norm. As a corollary we obtain a Dini-Lipschitz-type theorem forL1(G)convergence and we prove that the assumption on theL1(G)modulus of continuity in this theorem cannot be weakened. Similar results also hold for functions on the circle groupTand their (trigonometric) Fourier series.

Several representations for a complete residue system in the Euclidean domainZ(ω)are presented in this paper.

Seifert (4) demonstrated that every knot can be spanned by an orlentable surface. These Seifert surfaces lead to numerous knot invari- ants. The purpose of this paper is to demonstrate the existence of a parallel theory concerning connected nonorientable surfaces. These surfaces give rise to additional knot invariants. KEY WORDS AND PHRASES. Norieable surfaces, knot invariants, crosscaps and knots. AMS(MOS) SUBJECT CLASSIFICATIONS (1970). 55A25, 57C45. Submit your manuscripts at http://www.hindawi.com Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Mathematics Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Mathematical Problems in Engineering Hindawi Publishing Corporation http://www.hindawi.com Differential Equations International Journal of Volume 2014 Applied Mathematics Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Probability and Statistics Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Mathematical Physics Advances in Complex Analysis Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Optimization Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Combinatorics Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 International Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Operations Research Advances in

Letpandqdenote the number of vertices and edges of a graphG, respectively. LetΔ(G)denote the maximum degree ofG, andG¯the complement ofG. A graphGof orderpis said to be pancyclic ifGcontains a cycle of each lengthn,3≤n≤p. For a nonnegative integerk, a connected graphGis said to be of rankkifq=p−1+k. (Forkequal to0and1these graphs are called trees and unicyclic graphs, respectively.)In 1975, I posed the following problem: Givenk, find the smallest positive integerpk, if it exists, such that wheneverGis a rankkgraph of orderp≤pkandΔ(G)

This paper deals with the problem of finding solutions of the --._rstein integral equation. It is shown that this problem can be reduced to the study of the critical points of certain functional defined on L2(). Existence of a solution of the Hammersteln integral equation is proved. Some other related results of interest are obtained.

In this paper the author shows that a well known sufficient condition for strict cycliclty of a weighted shift onℓpis not a necessary condition for anypwith1

Some inequalities for the Wallis functions are proved. The results of this paper are consequences of some characterization of convex functions. A generalization of a result of Boyd (1) and an extentlon of an inequality of Gantschi (3) are obtained.

A theory is presented of the generation and propagation of the two and the three dimensional tsunamis in a shallow running ocean due to the action of an arbitrary ocean floor or ocean surface disturbance. Integral solutions for both two and three dimensional problems are obtained by using the generalized Fourier and Laplace transforms. An asymptotic analysis is carried out for the investigation of the principal features of the free surface elevation. It is found that the propagation of the tsunamis depends on the relative magnitude of the given speed of the running ocean and the wave speed of the shallow ocean. When the speed of the running ocean is less than the speed of the shallow ocean wave, both the two and the three dimensional free surface elevation represent the generation and propagation of surface waves which decay asymptotically ast−12for the two dimensional case and ast−1for the three dimensional tsunamis. Several important features of the solution are discussed in some detail. As an application of the general theory, some physically realistic ocean floor disturbances are included in this paper.

The purpose of this paper is to derive a nonlinear partial differential equation for whichλgiven by (1.3), is one value of the solution. In Section 2, we derive this equation using a straightforward dynamic programming approach. In Section 3, we discuss some computational aspects of derermining the solution of this equation. In Section 4, we show that the same method may be applied to the nonlinear characteristic value problem. In Section 5, we discuss how the method may by applied to find the higher characteristic values. In Section 5, we discuss how the same method may be applied to some matrix problems. Finally, in Section 7, we discuss selective computation.

For anyθwith0<θ<1, it is known that, for the set of all incomplete polynomials of typeθ, i.e,{p(x)=∑k=snakxk:s≥θ⋅n}, to have the Weierstrass property on[aθ,1], it is necessary thatθ2≤aθ≤1.In this paper, we show that the above inequalities are essentially sufficient as well.

The fundamental homomorphism theorem for rings is not generally applicable in hemiring theory. In this paper, we show that for the class ofN-homomorphism of hemirings the fundamental theorem is valid. In addition, the concept ofN-homomorphism is used to prove that every hereditarily semisubtractive hemiring is of type(K).

Some characteristic approximation properties of quadratic irrationals are studied in this paper. It is shown that the limit points of the sequenceδnform a subsetC(x), andD(x)can be generated fromC(x)in a relatively simple way. Another proof of Lekkerkerker's theorem is given using relations betweenδn−1,δn,δn+1which are independent ofxandn.

Once a food is processed it is subjected to a variable temperature-humidity-time distribution pattern which can cause further losses. If a truthful nutrition label is to be put on the food package knowledge of this distribution function is important in assessing the further loss that occurs. More important however, is some knowledge of the kinetics of the degradation of the particular nutrient being considered. The method presented in this paper is based on selecting certain criteria and then based on minimal data, decision rules are used to estimate the possible extent of loss. The steps are as follows: (1) Some estimate is made of the minimum, average and maximum temperatures and times for distribution of the food; (2) A decision is made as to whether moisture gain or loss is involved and can change the rate of degradation; (3) A literature search is made as to the kinetics of the degradation of the nutrient (even single point data, i.e., endpoint analysis are useful); (4) A decision is made as to the maximum amount of degradation tolerated for the average and maximum shelf life; (5) The amount of degradation in #4 is calculated based on both zero and first order rate constants estimated from #3; (6) If the amount lost is less than 50% in #5 then that data is used for the label. If it is greater, then the true order of the reaction must be determined in the lab for calculation in #5. Based on these rules a better estimate of losses can be made.

This paper demonstrates that, to first order, the optimum size of nuclear plant depends only on the form of the dependence of capital costs and availability with size and not on absolute levels; it is also independent of nuclear fuel costs. the advantage of this treatment is that the forms of these dependences are less controversial than absolute values and the scope for confusion in determining optimum size is therefore reduced.

A necessary and sufficient condition for a bounded operator to be a composition operator is investigated in this paper. Normal, quasi-hyponormal, paranormal composition operators are characterised.

Restricted isomorphism between two queueing systems implies that they have equivalent distribution function for at least one (but not all) output elements (e.g. waiting time, queue size, idle time, etc.). Quasi-isomorphism implies an approximate equivalence. Most of the single-server queueing systems can be approximated by a quasi-isomorphic system which has a gamma inter-arrival and gamma service distributions(Ep/Eq/1).This paper deals with the derivation of simpler isomorphs (in quasi-restricted sense) for such gamma-gamma(Ep/Eq/1)systems.

Letπb,c(x)denote the number of primes≤xand≡c(modb), and for positive integersxletΔb(x,c,l)=πb,c(x)−πb,l(x). Negative values ofΔ4(x,3,1)less than1012occur in six widely spaced regions. The first three regions, investigated by Leech [6], Shanks [9] and Lehmer [6 ], contain only a few thousand negative values ofΔ4(x,3,1). However, the authors [1] have recently discovered3new regions, the sixth occurring before20billion and containing more than half a billion negative values ofΔ4(x,3,1). In this paper numerical and graphical details of all six regions are given. Moreover, new results for the modulus8are presented. Previously, no negative values have been found forΔ8(x,c,1),c=3,5, or7and our search to1012reveals no such values forΔ8(x,3,1)orΔ8(x,7,1). ForΔ8(x,5,1)we have discovered the first two regions of negative values. The first of these regions, beginning atx=588067889, contains422,500negative values ofΔ8(x,5,1); the second occurs in the vicinity of35billion and contains more than a billion negative values ofΔ8(x,5,1).

The author considers one of the main problems in finite translation planes to be the identification of the abstract groups which can act as collineation groups and how those groups can act.The paper is concerned with the case where the plane is defined on a vector space of dimension2d overGF(q), whereqanddare odd. If the stabilizer of the zero vector is non-solvable, letG0be a minimal normal non-solvable subgroup. We suspect thatG0must be isomorphic to someSL(2,u)or homomorphic toA6orA7. Our main result is that this is the case whendis the product of distinct primes.The results depend heavily on the Gorenstein-Walter determination of finite groups having dihedral Sylow2-groups whendandqare both odd. The methods and results overlap those in a joint paper by Kallaher and the author which is to appear in Geometriae Dedicata. The only known example (besides Desarguesian planes) is Hering's plane of order27(i.e.,dandqare both equal to3) which admitsSL(2,13).

Suppose∑n=0∞anznhas radius of convergenceRandσN(z)=|∑n=N∞anzn|. Suppose|z1|<|z2|σN(z) for zϵT}. Two questions are asked: (a) canSbe cofinite? (b) canSbe infinite? This paper provides some answers to these questions. The answer to (a) is no, even ifT=z2. The answer to (b) is no, forT=z2ifliman=a≠0. Examples show (b) is possible ifT=z2and forTa neighborhood ofz2.