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The proposed simple modification of discrete homogeneous sliding-mode-based differentiators improves the accuracy and significantly lowers the output chattering in the absence of noises, while preserving the differentiation accuracy in their presence. The approach is extended to general discretely sampled homogeneous discontinuous systems. Numeric experiments confirm the theoretical results.

The purpose of this paper is to examine the non-zero distinct integral solutions of quinary biquadratic homogeneous diophantine equation x4 + y4 - (x + y)w3 = 14z2T2 in integers. In this paper, we present some different patterns of integral solutions to the above diophantine equation in five variables. Also, we obtain some properties as relations between solutions and special numbers.

A single homogeneous resource needs to be fairly shared between users that dynamically arrive and depart over time. Although good allocations exist for any fixed number of users, implementing these allocations dynamically is impractical: it typically entails adjustments in the allocation of every user in the system whenever a new user arrives. We introduce a dynamic fair resource division problem in which there is a limit on the number of users that can be disrupted when a new user arrives and study the trade-off between fairness and the number of allowed disruptions, using a fairness metric: the fairness ratio. We almost completely characterize this trade-off and give an algorithm for obtaining the optimal fairness for any number of allowed disruptions.

Homogeneity, which plays an essential role in decision making, economics and image processing, reflects the regularity of aggregation functions with respect to the inputs with the same ratio. Quasi-homogeneity is a relaxed homogeneity that reflects the original output as well as the same ratio. This paper is devoted to the characterization of all homogeneous/quasi-homogeneous binary aggregation functions in terms of single-argument functions.

Consider a homogeneous additive polynomial of the form F ( x ) = a 1 x 1 k + a 2 x 2 k + ⋯ + a s x s k , where the coefficients are integers. The function Γ ⁎ ( k ) is defined as the smallest number s of variables such that F is guaranteed to have a nontrivial zero in every p-adic field Q p regardless of the coefficients. In this article, we calculate the value of Γ ⁎ ( k ) for all 33 ≤ k ≤ 64 for which this value is not already known.

In this paper, we compare two procedures for allocating a sequence of fixed prizes in multi-stage nested Tullock contests, in which the number of prizes equals the number of contestants. In a winner-leave (loser-leave) procedure, in each stage, the prizes of the stage are allocated to winners (losers) according to their ranks, and prizes in early stages are higher (lower) than those in later stages. Players who obtain prizes leave the contest and the others proceed to the next stage of competition. For both procedures, it is effort-maximizing to allocate one prize in each stage. Provided that the positive prizes in the sequence are homogeneous, the optimally designed loser-leave procedure generates higher total effort if and only if the number of positive prizes is lower than a threshold. If the positive prizes in the sequence are heterogeneous, then the loser-leave procedure may generate higher total effort, even if the number of positive prizes in the sequence is in the high range.

The sacrum is often used for sex estimation of human remains. However, reported sexual classification accuracies based on the sacrum produce highly discrepant estimates ranging from 54% to 98% depending on the method and reference sample. Here, we therefore aim to evaluate the sacrum's efficacy in differentiating males from females by comparing three different approaches in a homogeneous Central European sample (n = 58, 27 males and 31 females) obtained from the 19th century Weisbach collection. Specifically, we investigated the sacrum by 1) a qualitative visual inspection, 2) traditional linear metrics, namely, sacral width, corpus width, and the associated corporo-basal index, and 3) geometric morphometrics (GM) using a 3D configuration of 100 landmarks and semilandmarks. Classification accuracies for the qualitative approach ranged from 69% to 81%. The investigated quantitative methods based on linear dimensions led to comparable classification accuracies of 62% for sacral width and 78% for the corporo-basal index. However, absolute corpus width had a stronger discriminative power (86%), similar to the PC scores from shape space (87%). Unexpectedly, the GM approach, which considered the shape of the entire sacrum, did not classify better than linear variables. This was exceeded only when sacrum shape was combined with corpus width or another measure of size, like the natural logarithm of the centroid size, yielding a classification accuracy of 95%. The male and female group means differed mainly in the general height-to-width relationship and corpus-to-alae proportions, corroborating patterns previously described in the literature. Our results suggest that the sacrum is markedly less effective than the hipbone for sex determination, which is at odds with its central position within the pelvic girdle and thus its supposed obstetric relevance.

In present article, under homogeneous Neumann boundary condition, we put forward a diffusive spruce budworm model with mixed delays and Holling II predation function firstly. Then, choosing delay (discrete delay or distributed delay) as bifurcating parameter together with characteristic equation, we derive that not only can discrete delay induce the appearance of Hopf bifurcations for this model, but also distributed delay can do it. However, to our knowledge, in the known literatures, Hopf bifurcation can only be deduced by discrete delay or distributed delay. So, the obtained results in present article are new. At last, by carrying out numerical simulations, we obtain periodic solutions and spatial patterns deduced by discrete delay or distributed delay, which illustrates the results in this article.

This paper deals with the finite-time state bounding problem of homogeneous nonlinear positive systems with disturbance. Based on a technique used in positive systems, explicit conditions are established such that all solutions of homogeneous nonlinear positive systems with degree 0 p 1 converge to a ball in finite time. The approach used in this paper is different from the usual Lyapunov-Krasovskii functional method. We also extend the main result to the general nonlinear time-varying systems. Finally, two numerical examples are given to show the effectiveness of our results.

The Ideal Profile Method (IPM) is a descriptive analysis in which consumers are asked to rate products on both their perceived and ideal intensities against a list of attributes. In addition, overall liking is rated. The information gathered from the IPM is rich, and directly actionable for product development. However, these data need special attention, since they are provided by consumers who are rating a fictive product. In order to fully appreciate the data, the Ideal Profile Analysis (IPA) has been set up. This methodology helps in (1) evaluating the consistency of the ideal data, (2) assessing homogeneous groups of consumers/products, (3) defining the sensory profile of the ideal product of reference, and (4) optimizing the products according to that reference.

The objective of the present work was to develop and evaluate fertilizing machine for vegetable to make under Egyptian condition. The fertilizing machine was evaluated versus four forward speeds (2.8, 3.2, 3.6, and 4.0 km/h), three feeding areas (50, 100, and 150 cm²), three fertilizing depths (15, 20, and 25 cm) and two bully diameters with land wheel (15 and 25 cm). The results showed that the highest productivity was 31.11 m³/fed; and 82.84% fertilizing homogeneous fertilizing obtained at 2.8 km/h forward speed, 150 cm² feeding area, 25 cm fertilizing depth and bully diameter with land wheel 15cm. The best result field efficiency was 85.12% and minimum specific energy 31.41kW.h/fed at obtained forward speed 4 km/h, 150cm² feeding area, 15 cm fertilizing depth and bully diameter with land wheel 15cm. The maximum consumption and operation cost was 128.78 LE/fed; and 5.79 LE/m³.

In this note we establish a necessary and sufficient condition for solvability of the homogeneous Riemann boundary problem with infinity index on a rectifiable open curve. The index of the problem we deal with considers the influence of the requirement of the solutions of the problem, the degree of non-smoothness of the curve at the endpoints as well as the behavior of the coefficient at these points.

We investigate fat projective linear codes over ${\mathbb Z}_{p^{m}}$ , $m\geqslant 2$ , with two nonzero homogeneous weights (“two-weight codes”), building on the graph theory approach developed by Delsarte for codes over fields. Our main result is the classification of such codes under the additional assumption that the columns of a generator matrix of the code determine a cap in the projective Hjelmslev geometry $\mathop {\mathrm {PHG}}\nolimits (k-1, {\mathbb Z}_{p^{m}})$ . This generalizes a result on projective two weight codes with dual distance at least four (Calderbank, 1982). The proof relies on a careful analysis of a certain strongly regular graph built on the cosets of the dual code, and on an interpretation of its parameters in terms of projective Hjelmslev geometry.

The purpose of this paper is to establish a necessary and sufficient condition for the boundedness of general product singular integral operators introduced by Han, Li and Lin [Y. Han, J. Li and C.-C. Lin, Criterion of the L 2 L^{2} boundedness and sharp endpoint estimates for singular integral operators on product spaces of homogeneous type, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 16 2016, 3, 845–907] on the multiparameter Lipschitz spaces of homogeneous type M ~ = M 1 × ⋯ × M n {\tilde{M}=M_{1}\times\cdots\times M_{n}} . Each factor space M i {M_{i}} , 1 ≤ i ≤ n {1\leq i\leq n} , is a space of homogeneous type in the sense of Coifman and Weiss. These operators generalize those studied by Journé on the Euclidean space and include operators studied by Nagel and Stein on Carnot–Carathéodory spaces. The main tool used here is the discrete Littlewood–Paley–Stein theory and almost orthogonality together with a density argument for the product Lipschitz spaces in the weak sense.

In this research article, two Haar wavelet collocation methods (HWCMs) (namely one dimensional HWCM and two dimensional HWCM) are adapted to approximate linear homogeneous and linear non-homogeneous Klein–Gordon equations. The results obtained from both methods are compared with exact solutions. Moreover, both of the methods are also compared together, that indicates much better performance of two dimensional Haar wavelet collocation method (2D HWCM) in a small number of collocation points.

In this research paper, we discuss systems of conformable linear differential equations. The conformable fundamental exponential matrix has been used to express the solution of the homogeneous and nonhomogeneous systems. The method of variation of parameters has been investigated to find the particular solution of the conformable system of nonhomogeneous linear differential equations. Several illustrative examples have been provided at the end of our study to validate all obtained results.

In this note, we obtain a reverse version of the integral Hardy inequality on metric measure spaces. Moreover, we give necessary and sufficient conditions for the weighted reverse Hardy inequality to be true. The main tool in our proof is a continuous version of the reverse Minkowski inequality. Also, we present some consequences of the obtained reverse Hardy inequality on the homogeneous groups, hyperbolic spaces and Cartan-Hadamard manifolds., 23 pages

Let G G be a locally compact group and let K K be its closed subgroup. Write G ^ K \widehat {G}_{K} for the set of irreducible representations with non-zero K K -invariant vectors. We call a pair ( G , K ) (G,K) admissible if for each irreducible representation ( π , V π ) (\pi , V_{\pi }) in G ^ K \widehat {G}_{K} , its K K -invariant subspace V π K V_{\pi }^{K} is of finite dimension. For each π \pi in G ^ K \widehat {G}_{K} , let π v i , ξ ¯ j \pi _{v_{i}, \overline {\xi }_{j}} ’s ( π v i , ξ ¯ j ( g K ) ≔ ⟨ v i , π ( g ) ξ j ⟩ ) (\pi _{v_{i}, \overline {\xi }_{j}}(gK)≔\langle v_{i}, \pi (g)\xi _{j}\rangle ) be the matrix coefficeints on G / K G/K induced by fixed orthonormal bases { v i } \{v_{i}\} and { ξ j } \{\xi _{j}\} for V π V_{\pi } and V π K V_{\pi }^{K} respectively. A probability measure μ \mu on G / K G/K is called a spectral measure if there is a subset Γ \Gamma of G ^ K \widehat {G}_{K} such that the set of all such matrix coefficients π v i , ξ ¯ j , π ∈ Γ , \pi _{v_{i}, \overline {\xi }_{j}},\ \pi \in \Gamma , constitutes an orthonormal basis for L 2 ( G / K , μ ) L^{2}(G/K, \mu ) with some suitable normalization of these matrix coordinate functions. In this paper, we shall give a characterization of a spectral measure for an admissible pair ( G , K ) (G,K) by using the Fourier transform on G / K G/K . Also, from this we show that there is a “local translation” (we call it locally regular representation in the sequel) of G G on L 2 ( G / K , μ ) L^{2}(G/K, \mu ) under a mild condition. This will give us some necessary conditions for the existence of spectral measures. In particular, the atomic spectral measures of finite supports for Gelfand pairs are studied.

We discuss practical methods for computing the space of solutions to an arbitrary homogeneous linear system of partial differential equations with constant coefficients. These rest on the Fundamental Principle of Ehrenpreis-Palamodov from the 1960s. We develop this further using recent advances in computational commutative algebra., 31 pages, 1 figure

We introduce the concepts of Cohen positive strongly p -summing and positive p -dominated m-homogeneous polynomials. The version of Pietsch’s domination theorem for the first class among other results and a Bu-type theorem is proved, as well as some inclusions with other known spaces. Moreover, we present a characterization of these classes in tensor terms.

We present a complete algorithm that computes all hypergeometric solutions of homogeneous linear difference equations and rational solutions of parameterized linear difference equations in the setting of Π Σ ⁎ -fields. More generally, we provide a flexible framework for a big class of difference fields that are built by a tower of Π Σ ⁎ -field extensions over a difference field that enjoys certain algorithmic properties. As a consequence one can compute all solutions in terms of indefinite nested sums and products that arise within the components of a parameterized linear difference equation, and one can find all hypergeometric solutions of a homogeneous linear difference equation that are defined over the arising sums and products.

De Vylder and Goovaerts (2000) made a conjecture on the comparison of the finite time ruin probability in a homogeneous risk model and the corresponding ruin probability in an associated model with equalized claim amounts. The conjecture, however, remains an open problem. In this paper, we provide a conjecture that is stronger than De Vylder and Goovaerts' conjecture and also provide sufficient conditions for the conjectures, which are more mathematically tractable than De Vylder and Goovaerts' conjecture and thus easier to work with. By using the sufficient conditions for the conjectures, we solve De Vylder and Goovaerts' conjecture when n = 3 , where n is the number of claims in the finite time.

Considering individuals’ aggregation behavior, we study the SIS (Susceptible-Infected-Susceptible) epidemic model in a modified activity driven network (ADN). The relations among individuals are divided into three categories: strong links (SLs), the first kind of weak links (FWLs) and the second kind of weak links (SWLs). Based on the mean field approximation, we theoretically calculate the epidemic threshold condition while the strong links structure is a homogeneous or a heterogeneous network, respectively. Finally, we provide some numerical examples that support our theoretical results.

The refined estimates of all homogeneous expansions for a subclass of biholomorphic starlike mappings are mainly established on the unit ball in complex Banach spaces or the unit polydisk in ℂn with a unified method. Especially the results are sharp if the above mappings are further k-fold symmetric starlike mappings or k-fold symmetric starlike mappings of order α. The obtained results unify and generalize the corresponding results in some prior literatures.

PURPOSE To derive the isodose line R relative to the prescription dose below which irradiated normal tissue (NT) regions benefit from a hypofractionated schedule with an isoeffective dose to the tumor. To apply the formalism to clinical case examples. METHODS From the standard biologically effective dose (BED) equation based on the linear-quadratic (LQ) model, the BED of an NT that receives a relative proportion r of the prescribed dose per fraction for a given α/β-ratio of the tumor, (α/β)T , and NT, (α/β)NT , is derived for different treatment schedules while keeping the BED to the tumor constant. Based on this, the "break-even" isodose line R is then derived. The BED of NT regions that receive doses below R decreases for more hypofractionated treatment schedules, and hence a lower risk for NT injury is predicted in these regions. To assess the impact of a linear behavior of BED for high doses per fraction (>6 Gy), we evaluated BED also using the LQ-linear (LQ-L) model. RESULTS The formalism provides the equations to derive the BED of an NT as function of dose per fraction for an isoeffective dose to the tumor and the corresponding break-even isodose line R. For generic α/β-ratios of (α/β)T = 10 Gy and (α/β)NT = 3 Gy and homogeneous dose in the target, R is 30%. R is doubling for stereotactic treatments for which tumor control correlates with the maximum dose of 100% instead of the encompassing isodose line of 50%. When using the LQ-L model, the notion of a break-even dose level R remains valid up to about 20 Gy per fraction for generic α/β-ratios and DT=2(α/β) . CONCLUSIONS The formalism may be used to estimate below which relative isodose line R there will be a differential sparing of NT when increasing hypofractionation. More generally, it allows to assess changes of the therapeutic index for sets of isoeffective treatment schedules at different relative dose levels compared to a reference schedule in a compact manner.

We establish the most general Szasz type estimates for homogeneous Besov and Lizorkin-Triebel spaces, and their realizations.

In this paper, motivated by considerations of server utilization and energy consumption in cloud computing, we investigate a homogeneous queueing system with a threshold-based workload control sche...

In this paper we study Toeplitz and Ces\`aro-type operators on holomorphic function spaces on a homogeneous Siegel domain of Type II. We prove several necessary conditions and sufficient conditions for these operators to be continuous or compact, or to belong to suitable Schatten classes., Comment: 25 pages, no figures

A novel space–time generalized finite difference method based on the direct space–time discretization technique is developed for solving dynamic coupled thermoelasticity problems. By considering the time scale as an additional space dimension, the spatial and temporal domains are simultaneously discretized. In our numerical implementation, the velocity is introduced as an additional unknown field quantity for dealing with the inertia item appearing in elastodynamic equations. Some dynamic coupled thermoelasticity problems in homogeneous or heterogeneous plates under different loading cases are numerically analyzed by this method. The accuracy of the present method is verified by comparison with analytical solutions or other numerical results.

This paper concerns the existence of bounded classical solutions to the attraction-repulsion chemotaxis system with logistic source (⋆) { u t = Δ u − χ ∇ ⋅ ( u ∇ v ) + ξ ∇ ⋅ ( u ∇ w ) + f ( u ) , x ∈ Ω , t > 0 , 0 = Δ v − β v + α u , x ∈ Ω , t > 0 0 = Δ w − δ w + γ u , x ∈ Ω , t > 0 in a smooth bounded domain Ω ⊆ R N ( N ≥ 1 ) , subject to nonnegative initial data and homogeneous Neumann boundary conditions, where f ( u ) ≤ a − b u r for all u ≥ 0 with some a ≥ 0 , b > 0 and r ≥ 1 . Here χ , α , ξ , β as well as γ and δ are positive constants. It is proved that the corresponding system ( ⋆ ) possesses a unique global bounded classical solution in the balance case χ α = ξ γ with r > 2 N − 2 N or, the attraction domination case ξ α > ξ γ with b ≥ ( N − 2 ) + N ( χ α − ξ γ ) and r = 2 , respectively. The study of this paper improves the results in Li-Xiang (2016) [12] , Xu-Zheng (2018) [39] , Wang (2016) [26] as well as Zhao et al. (2017) [42] and Tello-Winkler (2007) [23] , in which, the assumption b > ( N − 2 ) + N ( χ α − ξ γ ) (see Li-Xiang (2016) as well as Wang (2016) and Zhao et al. (2017)) or b > ( N − 2 ) + N χ (see Tello-Winkler (2007)) or r > 2 N + 2 N + 2 (see Xu-Zheng (2018)) or r > N 2 + 4 N − N 2 (see Li-Xiang (2016)) are intrinsically required.

We prove an analogue of the classical zero-one law for both homogeneous and nonhomogeneous Markov chains (MC). Its almost precise formulation is simple: given any event A from the tail σ-algebra of...

Статья представляет собой обзор результатов автора о строении ортогонально аддитивных однородных полиномов в векторных, банаховых и квазибанаховых решетках. В ходе изложения приводится сравнительный анализ с результатами других авторов, занимающихся данным направлением. Метод исследования, основанный на линеаризации посредством степени векторной решетки и канонического ортогонально аддитивного полинома, представлен в \S 1. Далее, в \S 2 приводится несколько непосредственных приложений этого метода к ортогонально аддитивным однородным полиномам: критерий интегральной представимости, существование одновременного продолжения с мажорирующей подрешетки, характеризация крайних продолжений. \S 3 содержит полное описание и мультипликативное представление однородных полиномов, сохраняющих дизъюнктность. \S 4 посвящен решению проблемы компактного и слабо компактного доминирования (мажорации) для однородных полиномов в банаховых решетках. В \S 5 рассматриваются свойства выпуклости и вогнутости индивидуального ортогонально аддитивного однородного полинома между квазибанаховыми решетками, а в \S 6 выясняются условия, при которых квазибанахова решетка однородных ортогонально аддитивных полиномов является $(p,q)$-выпуклой, $(p,q)$-вогнутой, геометрически выпуклой. В \S 7 дается характеризация и аналитическое описание полиномов, допускающих представление в виде конечной суммы полиномов, сохраняющих дизъюнктность. Наконец, в \S 8 сформулированы нерешенные задачи, представляющие существенный интерес для дальнейшего развития теории.

In this research we prove an existence result of renormalized solutions for nonlinear parabolic equations with two lower order terms and $$L^1$$ -data under the functional framework of the Musielak–Sobolev spaces in cylindrical domains with homogeneous Dirichlet boundary condition.

Based on the performed researches the method of decomposition of graphs of total electric loading of power system with application of a method of Hilbert-Huang is improved. This approach allows obtaining a homogeneous basic component of electrical load and temperature component, which has a close correlation with air temperature, which improves the accuracy of short-term forecasting. The results of testing the developed mathematical model are given. Ref. 9, fig. 1, table.

We obtain the characterizations of commutators of several versions of maximal functions on spaces of homogeneous type. In addition, with the aid of interpolation theory, we provide weighted version of the commutator theorems by establishing new characterizations of the weighted BMO space. Finally, a concrete example shows that the local version of commutators also has an independent interest.

Series and limits were used to calculate the centre of mass of homogeneous circular sector plates. The method presented can be used to teach students about discrete and continuous systems.

When the scale parameters and skewness parameters are unknown, we consider the problem of homogeneous test of location parameters in several skew-normal populations. First, the conditional test sta...

Let $$(X, d, \mu)$$ be a space of homogeneous type. Let $$T_{1}, T_{2}$$ be singular integral operators with nonsmooth kernels. By establishing sparse domination, we obtain quantitative boundedness for the composite operator $$T_{1}T_{2}$$ on $$L^{p}(X, \omega)$$ with $$\omega\in A_{p}$$ and the weighted endpoint estimate for the composite operator $$T_{1}T_{2}$$ .