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This paper introduces strong bisimulation for continuous-time Markov decision processes (CTMDPs), a stochastic model which allows for a nondeterministic choice between exponential distributions, and shows that bisimulation preserves the validity of CSL. To that end, we interpret the semantics of CSL - a stochastic variant of CTL for continuous-time Markov chains - on CTMDPs and show its measure theoretic soundness. The main challenge faced in this paper is the proof of logical preservation that is substantially based on measure theory.

The paper explores the uniqueness properties of the subjective probabilities in two axiomatizations of state-dependent preferences. Karni, Schmeidler, and Vind's (KSV 1983) system depends on selecting an arbitrary auxiliary probability, and as such, does not guarantee the uniqueness of the derived subjective probability. However, an axiom system initially designed by Karni and Schmeidler (KS 1981) and further elaborated upon here does guarantee the desired uniqueness as well as a useful property of “stability” of the derived solution. When the preference relation displays state-independence, even the KS probabilities may not agree with those derived from the classic Anscombe-Aumann (AA 1963) theorem. However, we claim that, in this case, the KS rather than the AA probabilities are the appropriate representation of the agent's beliefs.

In this paper, the problem of approximating a function defined on a finite subset of the real line by a family of generalized rational functions whose numerator and denominator spaces satisfy the Haar conditions on some closed interval [a, b] containing the finite set is considered. The pointwise closure of the family restricted to the finite set is explicitly determined. The representation obtained is used to analyze the convergence of best approximations on discrete subsets of [a, b] to best approximations over the whole interval (as the discrete subsets become dense) in the case that the function approximated is continuous on [a, b] and the rational family consists of quotients of algebraic polynomials. It is found that the convergence is uniform over [a, b] if the function approximated is a so-called normal point. Only L p {L_p} norms with 1 ⩽ p > ∞ 1 \leqslant p > \infty are employed.

In this paper, several characterizations for s-closed spaces are obtained using regular semiclosed sets and some sets having two properties of near openness and near closedness in the same time. Images of s-closed spaces under some noncontinuous mappings are investigated. The relations between s-closedness and near compactness, co-compactness, almost co-compactness, light compactness, mild compactness are obtained. S-closed subsets relative to a semi-T2-spaces are also discussed. في هذا البحث بعض الخواص الجديدة لفراغات س - المغلقة التي قدمها طومسون عام 1967 ، وذلك باستخدام بعض المجموعات التي لها خاصية قريبة الانفتاح وقريبة الانغلاق في آن واحد ، كما تم مناقشة صور الفراغات س - المغلقة تحت تأثير بعض الرواسم غير المتصلة ، كما تضمن البحث دراسة عن علاقة الانغلاق السيني ببعض أنواع الأصماط ، واحتوى البحث كذلك على مناقشة للمجموعات الجزئية السينية المغلقة بالنسبة لفراغ T2 النصفي .

In this paper, we characterize the class of all spaces X whose products with a fixed non-Archimedan space Y are normal. In particular, we give a characterization of all spaces X whose products with every ω μ -metrizable space are normal.

The main motivation of this paper is to investigate some properties of the generating functions for the numbers Yn(λ) and the polynomials Yn(x; λ), which were recently introduced by Simsek [9] and so we give some identities and relations including the numbers Yn(λ) and the polynomials Yn(x; λ), the Bernoulli numbers and polynomials, the Apostol-Bernoulli numbers and polynomials, the Apostol-Euler numbers and polynomials, the Stirling numbers.

Five years ago in San Diego, USA, a Wheat Industry Utilization Conference took place under the direction of Y. Pomeranz who published the presented papers under the title Wheat is Unique.1 The information gathered in that publication still represents today the present state of knowledge on the structure, composition, processing, end-use properties and products of wheat. This is also true of the topics discussed here, the extraction of starch and gluten from wheat and extrusion cooking, on which the present author contributed two conference papers.2,3 Therefore, as only a few new findings can be reported, this chapter will concentrate on presenting the current state of knowledge on these topics with special reference to the functional characteristics of wheat gluten and starch. In so doing, the process technological possibilities for the extraction of starch and gluten from wheat flours and wheat wholemeal flours as well as the application of wheat starch and wheat flours for the manufacture of extrusion cooking products will be emphasized. Special emphasis is also given to the gluten-forming properties of wheat proteins and the two starch fractions present in the endosperm which differ not only in size but also in physical and chemical properties.

This paper introduces a parametric method for identifying the somatosensory evoked potentials (SEPs). The identification was carried out by using pole-zero modeling of the SEPs in the discrete cosine transform (DCT) domain. It was found that the DCT coefficients of a monophasic signal can be sufficiently approximated by a second-order transfer function with a conjugate pole pair. The averaged SEP signal was modeled by the sum of several second-order transfer functions with appropriate zeros and poles estimated using the least square method in the DCT domain. Results of the estimation demonstrated that the model output was in an excellent agreement with the raw SEPs both qualitatively and quantitatively. Comparing with the common autoregressive model with exogenous input modeling in the time domain, the DCT domain modeling achieves a high goodness of fitting with a very low model order. Applications of the proposed method are possible in clinical practice for feature extraction, noise cancellation and individual component decomposition of the SEPs as well as other evoked potentials.

A path in an edge-colored graph is called conflict-free if it contains a color that is used by exactly one of its edges. An edge-colored graph G is conflict-free connected if for any two distinct vertices of G, there is a conflict-free path connecting them. For a connected graph G, the conflict-free connection number of G, denoted by cfc(G), is defined as the minimum number of colors that are required to make G conflict-free connected. In this paper, we investigate the conflict-free connection numbers of connected claw-free graphs, especially line graphs. We use L(G) to denote the line graph of a graph G. In general, the k-iterated line graph of a graph G, denoted by \(L^k(G)\), is the line graph of the graph \(L^{k-1}(G)\), where \(k\ge 2\) is a positive integer. We first show that for an arbitrary connected graph G, there exists a positive integer k such that \(cfc(L^k(G))\le 2\). Secondly, we get the exact value of the conflict-free connection number of a connected claw-free graph, especially a connected line graph. Thirdly, we prove that for an arbitrary connected graph G and an arbitrary positive integer k, we always have \(cfc(L^{k+1}(G))\le cfc(L^k(G))\), with only the exception that G is isomorphic to a star of order at least 5 and \(k=1\). Finally, we obtain the exact values of \(cfc(L^k(G))\), and use them as an efficient tool to get the smallest nonnegative integer \(k_0\) such that \(cfc(L^{k_0}(G))=2\).

We analyze the explicit contribution of fluid inertia and fluid unsteadiness to the force acting on a solid sphere moving in a vertical solid-body rotation flow, in the limit of small Reynolds and Taylor numbers. This problem can be thought of as a test case where the flow induced by the particle is both unsteady (in the laboratory frame) and convected by the unperturbed flow. Many authors assume that the contributions of these two effects can be approximately superposed, and postulate that the particle motion equation is composed of the classical Boussinesq-Basset-Oseen equation (obtained by neglecting the fluid inertia) plus an additive lift force. In the present paper the simplicity of the unperturbed flow enables one to calculate analytically the explicit contribution of each term appearing in the perturbed flow equation (by using matched asymptotic expansions). Our results show how the convective terms and the unsteady term do contribute to the particle drag and lift coefficients in a very complex and nonadditive manner.

In this paper our aim is to give refinements of Jensen?s type inequalities for the convex function defined on the co-ordinates of the bidimensional interval in the plane.

A compact microwave bandpass filter with λ/4 stepped impedance resonators (SIRs) is presented in this paper. λ/4 SIRs are employed here not only to miniaturize the circuit size, but also to eliminate spurious resonance at 2f 0 . To achieve the maximal number of finite transmission zeros, this filter is synthesized based on the 4th-order fully canonical coupling topology. As a result, four finite transmission zeroes are analytically achieved, and used to sharpen filter rejection skirts. Three capacitive J couplings are systematically designed to meet the required coupling strengths for the filter frequency response. Besides, they also adjust their coupling zeros for 3f 0 spurious suppression. Lastly, a 4th-order fully canonical bandpass filter is designed and fabricated with central frequency of 1.8 GHz and fractional bandwidth of 11.0% The proposed filter possesses preferred merits: compact size, 4 transmission zeros and up to 4.8f 0 20 dB attenuated stopband.

Wide field application of curve number (CN) methodology in design flood estimation and forecasting studies is a well-accepted reality. The parameter CN is often regarded as a constant, but it is in fact a random variable, for it relies on a number of factors governing the process of rainfall-runoff. This paper suggests an alternative procedure to estimate design runoff (Q) using design storm (P) and design curve number (CN) values. To this end, design CN values for different durations and return periods have been derived from 25 years of daily annual maximum P-Q data of 10 Indian catchments. When compared, the computed design Q from design CN values was either very close to or slightly greater than the observed Q. The performance is also evaluated using coefficient of determination (R2), percentage of bias (PBIAS), and normalized Nash-Sutcliffe efficiency (NNSE). The magnitude of design CN is found to decrease for longer durations and smaller return periods, and vice versa, and such a behavior invoked the development of an empirical relation for estimation of design CN from given return period and duration for gauged as well as ungauged watersheds. The statistical analysis revealed the general extreme value (GEV) to fit best the P-CN series, whereas multiple probability distributions, viz., GEV, Gumbel max, log Pearson 3, and Gen Pareto fitted best the Q series. The 50-year, 100-year, and 200-year runoff estimated from the P-CN series exceeded only marginally those derived from the conventional Q series approach.

One of the objects of the paper which last year I had the honour of presenting to the Royal Society, was to shew the in­ sufficiency in mathematical reasoning, of a principle of analogy, by which the properties demonstrated for one figure were to be transferred to another, to which the former was supposed to bear a resemblance; and the argument for the insufficiency of the principle was this, that the analogy between the two figures was neither antecedent to calculation, nor independent of it, and consequently could not regulate it; that analogy was the object of investigation, not the guide; the result of demonstra­tion, not its directing principle. Having shewn that analogy could not establish the truth of certain mathematical conclusions, I next endeavoured to shew why such conclusions had been rightly inferred; not by pro­posing any new excogitated principle, nor by pointing out an hitherto unobserved intellectual process; but I conceived they might be obtained by operations conducted in a manner similar to that by which all reasoning with general terms is conducted, and that the relations between the symbols or general terms were to be established by giving the true meaning to the con­necting signs, which indicate not so much the arithmetical computation of quantities, as certain algebraical operations. It was further observed, that, from certain established formulas, abridged symbols or general terms might be formed, which consequently must have their signification dependent on such formulas; and that, although the parts of certain abridged ex­pressions could not separately be arithmetically computed, yet the expressions themselves might be legitimately employed in all algebraic operations.

My Dear Sir, In a Memoir which I had the honour to present to you two years ago, I related some experiments on trees, from which I inferred, that their sap, having been absorbed by the bark of the root, is carried up by the alburnum or white wood, of the root, the trunk, and the branches; that it passes through what are there called the central vessels, into the succulent part of the annual shoot, the leaf-stalk, and the leaf; and that it returns to the bark, through the returning vessels of the leaf-stalk. The principal object of this Paper is, to point out the causes of the descent of the sap through the ’bark, and the consequent formation of wood. These causes appear to be, gravitation, motion communicated by winds or other agents, capillary attraction, and probably something in the conformation of the vessels themselves, which renders them better calculated to carry fluids in one direction than in another. I shall begin with a few observations on the leaf, from which all the descending fluids in the tree appear to be derived. This organ has much engaged the attention of naturalists, particularly of M. Bonnet: but their experiments have chiefly been made on leaves severed from the tree; and, therefore, whatever conclusions have been drawn, stand on very questionable ground. The efforts which plants always make to turn the upper surfaces of their leaves to the light, have with reason induced naturalists to conclude, that each surface has a totally distinct office; and the following experiments tend strongly to support that conclusion.

My Dear Sir, It is well known that the fluid, generally called the Sap in trees, ascends in the spring and summer from their roots, and that in the autumn and winter it is not, in any considerable quantity, found in them; and I have observed in a former Paper, that this fluid rises wholly through the alburnum, or sap-wood. But Du Hamel and subsequent naturalists have proved, that trees contain another kind of sap, which they have called the true, or peculiar juice, or sap of the plant. Whence this fluid originates does not appear to have been agreed by naturalists; but I have offered some facts to prove that it is generated by the leaf; and that it differs from the common aqueous sap owing to changes it has undergone in its circulation through that organ: and I have contended that from this fluid ( which Du Hamel has called the suc propre , and which I will call the true sap,) the whole substance, which is annually added to the tree, is derived. I shall endeavour in the present Paper to prove that this fluid, in an inspissated state, or some concrete matter deposited by it, exists during the winter in the alburnum, and that from this fluid, or substance, dissolved in the ascending aqueous sap, is derived the matter which enters into the composition of the new leaves in the spring, and thus furnishes those organs, which were not wanted during the winter, but which are essential to the further progress of vegetation. Few persons at all conversant with timber are ignorant, that the alburnum, or sap-wood of trees, which are felled in the autumn or winter, is much superior in quality to that of other trees of the same species, which are suffered to stand till the spring, or summer: it is at once more firm and tenacious in its texture, and more durable. This superiority in winterfelled wood has been generally attributed to the absence of the sap at that season; but the appearance and qualities of the wood seem more justly to warrant the conclusion, that some substance has been added to, instead of taken from it, and many circumstances induced me to suspect that this substance is generated, and deposited within it, in the preceding summer and autumn.

When I had ascertained that carbonaceous substances, whether vegetable, animal, or mineral, were capable of being converted into a product, which, by its effects on earthy and metallic solutions, on dissolved gelatine, and on skin, resembled the natural vegetable principle called Tannin , I was at first inclined to give it the name of artificial or factitious tannin ; but some eminent chemists of this country, for whose opinions I have the highest respect, considered this name as objectionable; for although the artificial substance resembles tannin in the parti­culars above stated, yet in one character there appears to be a very considerable difference, namely, the effect of nitric acid; for by this, the artificial substance is, whilst the varieties of natural tannin are destroyed . Such an objection, sanctioned by such authority, induced me to alter the title of my Paper, and to expunge the word tannin wherever it had been applied to the artificial product. In order to satisfy myself more fully on this point, I have, since the communication of my former Paper, made a few ex­periments on the comparative effects produced by nitric acid on those substances which contain the most notable quantities of tannin , and of these I shall now give a succinct account, and shall also cursorily notice other experiments, in which a tanning substance has been produced, under circumstances different, in some measure, from those which have been already described.