Search

In this paper, we will consider an arithmetical approach to the Eratosthenes sieve and to the problem of the twin primes.

The aim of this paper is to study, by using the mathematical tools developed by Chałupnik, Touzé, and Van der Kallen, the effect of the Frobenius twist on $\operatorname{Ext}$-group in the category of strict polynomial functors. As an application, we obtain explicit formulas of cohomology of the orthogonal groups and symplectic ones.

In this paper we first establish global pointwise time-space estimates of the fundamental solution for Schr\"odinger equations, where the symbol of the spatial operator is a real non-degenerate elliptic polynomial. Then we use such estimates to establish related Lp-Lq estimates on the Schr\"odinger solution. These estimates extend known results from the literature and are sharp. This result was latetly already generalized to a degenerate case (cf. [9]).

In this paper, we classify the invariant complex structures on four-dimensional, solvable, simply-connected real Lie groups with commutator of dimension three. The resulting complex surfaces corresponding to these structures are also determined. The classification is based on the determination of certain complex subalgebras of the complexifications of the corresponding real Lie algebras.

The question of which functions acting entrywise preserve positive semidefiniteness has a long history, beginning with the Schur product theorem [Crelle 1911], which implies that absolutely monotonic functions (i.e., power series with nonnegative coefficients) preserve positivity on matrices of all dimensions. A famous result of Schoenberg and of Rudin [Duke Math. J. 1942, 1959] shows the converse: there are no other such functions. Motivated by modern applications, Guillot and Rajaratnam [Trans. Amer. Math. Soc. 2015] classified the entrywise positivity preservers in all dimensions, which act only on the off-diagonal entries. These two results are at "opposite ends", and in both cases the preservers have to be absolutely monotonic. We complete the classification of positivity preservers that act entrywise except on specified "diagonal/principal blocks", in every case other than the two above. (In fact we achieve this in a more general framework.) This yields the first examples of dimension-free entrywise positivity preservers - with certain forbidden principal blocks - that are not absolutely monotonic., Minor edits in exposition, 19 pages. The paper now uses the style file of Trans. AMS (to appear)

Accurate sky identification is one of the most important functions of an automated telescope mount. The more accurately the robotic telescope is navigated to the investigated part of the sky, the better the observations and discoveries made. In this paper, we present mathematical methods for accurate sky identification (celestial coordinates determination). They include the automatic selection of the reference stars, preliminary and full sky identification, as well as an interaction with international databases, which are a part of the astrometric calibration. All described methods help to receive accurately calculated astrometric data and use it for the positional calibration and better navigation of the automated telescope mount. The developed methods were successfully implemented in the Collection Light Technology (CoLiTec) software. Through its use, more than 1600 small solar system objects were discovered. It has been used in more than 700,000 observations and successful sky identifications, during which, five comets were discovered. Additionally, the accuracy indicators of the processing results of the CoLiTec software are provided in the paper, which shows benefits of the CoLiTec software and lower standard deviation of the sky identification in the case of low signal-to-noise ratios.

This paper extends the results from a work of Hytönen, Petermichl, and Volberg about sharp A 2 A_2 - A ∞ A_\infty estimates with matrix weights to the non-homogeneous situation.

In 1979, Pisier proved remarkably that a sequence of independent and identically distributed standard Gaussian random variables determines, via random Fourier series, a homogeneous Banach algebra P strictly contained in C(T), the class of continuous functions on the unit circle T and strictly containing the classical Wiener algebra A(T), that is, A(T)⫋P⫋C(T). This improved some previous results obtained by Zafran in solving a long-standing problem raised by Katznelson. In this paper, we extend Pisier’s result by showing that any probability measure on the unit circle defines a homogeneous Banach algebra contained in C(T). Thus Pisier algebra is not an isolated object but rather an element in a large class of Pisier-type algebras. We consider the case of spectral measures of stationary sequences of Gaussian random variables and obtain a sufficient condition for the boundedness of the random Fourier series ∑ n∈Zfˆ(n)ξnexp(2πint) in the general setting of dependent random variables (ξn).

Let a reductive groupG act linearly on a vectorspaceV, and letO∋V be an orbit. For each irreducible representation ω ofG, the multiplicity with which ω occurs in the ring of regular functions onO (or on its closureŌ) provides an interesting numerical invariant ofO. We introduce an algebraic notion of a “deformation” of an orbit into another one. The main goal of this paper is to give sufficient conditions on an orbit, in order that an arbitrary deformation of this orbit has to preserve all the multiplicites mentioned above.

In this paper some non existence results are given for smooth varieties of dimension bigger then 1, embedded in projective spaces with low codimension, by the pluricanonical system |mK X |, withm≥2. The only meaningful cases of codimension 2 are surfaces in P4 and threefolds in P5, whose existence is excluded. When the codimension is 3, for surfaces in P5 is proven thatm=2, while for three-folds in P6 and fourfolds in P7 only two numerical possibilities for the degree are given.

The Tarski number of a non-amenable group G is the minimal number of pieces in a paradoxical decomposition of G. In this paper we investigate how Tarski numbers may change under various group-theoretic operations. Using these estimates and known properties of Golod-Shafarevich groups, we show that the Tarski numbers of 2-generated non-amenable groups can be arbitrarily large. We also use the cost of group actions to show that there exist groups with Tarski numbers 5 and 6. These provide the first examples of non-amenable groups without free subgroups whose Tarski number has been computed precisely., 26 pages. v4: We have added the result about the existence of groups with Tarski number 5 which previously appeared in a separate paper of the second author arXiv:1406.2097. Section 5 has been rewritten. Minor changes in Appendix B. We also replaced left group actions by right group actions

This paper studies the $$\mathcal {M}_0$$ -shadowing property for two types of volume-preserving diffeomorphisms defined on compact manifolds. For symplectic diffeomorphisms defined on symplectic manifolds, the $$C^1$$ -interior of the set of all symplectic diffeomorphisms with the $$\mathcal {M}_0$$ -shadowing property is described by the set of the Anosov diffeomorphisms. If a volume-preserving diffeomorphism in $$\mathrm{Diff}^1_{\mu }(M)$$ is a $$C^1$$ -stable $$\mathcal {M}_0$$ -shadowing diffeomorphism, then M admits a volume-hyperbolic dominated splitting.

In the present paper, a necessary and sufficient condition for an element of the semigroup BX (D) defined by semilattices of the class Σ1(X, 5) to be regular is given. Moreover, formulas for calculation of regular elements are derived.

Given a finite poset $\mathcal P$, we call a family $\mathcal F$ of subsets of $[n]$ $\mathcal P$-saturated if $\mathcal F$ does not contain an induced copy of $\mathcal P$, but adding any other set to $\mathcal F$ creates an induced copy of $\mathcal P$. The induced saturated number of $\mathcal P$, denoted by $\text{sat}^*(n,\mathcal P)$, is the size of the smallest $\mathcal P$-saturated family with ground set $[n]$. In this paper we are mainly interested in the four-point poset called the butterfly. Ferrara, Kay, Kramer, Martin, Reiniger, Smith and Sullivan showed that the saturation number for the butterfly lies between $\log_2{n}$ and $n^2$. We give a linear lower bound of $n+1$. We also prove some other results about the butterfly and the poset $\mathcal N$., Comment: 13 pages

The exponential and Cayley maps on SE(3) are the prevailing coordinate maps used in Lie group integration schemes for rigid body and flexible body systems. Such geometric integrators are the Munthe–Kaas and generalized- α schemes, which involve the differential and its directional derivative of the respective coordinate map. Relevant closed form expressions, which were reported over the last two decades, are scattered in the literature, and some are reported without proof. This paper provides a reference summarizing all relevant closed-form relations along with the relevant proofs, including the right-trivialized differential of the exponential and Cayley map and their directional derivatives (resembling the Hessian). The latter gives rise to an implicit generalized- α scheme for rigid/flexible multibody systems in terms of the Cayley map with improved computational efficiency.

This study provides a systematic literature review of research in the field of teaching and learning mathematics through Content and Language Integrated Learning (CLIL), Content-Based Instruction (CBI), and English Medium Instruction (EMI). The review aims to examine the most relevant literature with a focus on mathematics and CLIL, CBI, or EMI in Scopus and Web of Science per the Preferred Reporting Items for Systematic Reviews (PRISMA) guidelines. Based on 151 sources, 52 papers were selected according to predefined selection criteria. The papers were analysed and coded according to the following categories: (1) geographical productivity, (2) diachronic productivity growth, (3) main objectives, (4) methodology, and research design, (5) variables and measurement instruments, (6) context and sample details, and (7) main findings. The results reveal that most of the research analysed has been carried out in the Asian continent, followed by Europe. The analysis of diachronic productivity shows that the study of the application of CLIL, CBI, and EMI programs in the teaching-learning process of mathematics has notably increased in recent years, especially in the last triennium (2020–2022). Regarding the objectives of the selected corpus, the majority aimed at teaching practices and learning processes, and outcomes in mathematics and language proficiency in CLIL, CBI, and/or EMI classrooms. The corpus analysed fits within one or more of the following categories: empirical, qualitative, descriptive, correlational, and cross-sectional. The samples utilized in different studies differ significantly, both in terms of quantity –ranging from one person to 700– and in the educational level being studied, which would be primary, secondary, or tertiary education. The main variables studied in the corpus focus on mathematical competence, language proficiency, teaching practices, teacher training, science competence, and teachers’ perceptions. The most widely used instruments have been objective tests, such as questionnaires, together with standardized tests to measure some aspects related to mathematical competence and language proficiency. They are followed by an analysis of documents (academic records, teaching materials, official documents...), participant or non-participant observation, interviews, and video and audio recordings. In summary, in the scientific literature analysed, a positive or neutral view predominates on the effects of the CLIL, CBI, and EMI approaches on the learning of mathematics and the L2. This can be due to methodological issues fundamentally related to the methodology, research design, sample, and measurement instruments. Thus, we must highlight that some of the results from the selected papers must be interpreted with caution. Taking this factor into consideration, further comparative studies on a wider scale are required to examine thoroughly the effects of CLIL, CBI, and EMI on the teaching and learning of mathematics in an L2. Besides, it is important to study in greater depth the different levels of language acquisition since the research analysed shows that these have not been sufficiently addressed in the mathematical field of knowledge.

This paper presents a curvature-free version of the Log ( 2 k − 1 ) \text {Log}(2k-1) Theorem of Anderson, Canary, Culler, and Shalen [J. Differential Geometry 44 (1996), pp. 738–782]. It generalizes a result by Hou [J. Differential Geometry 57 (2001), no. 1, pp. 173–193] and its proof is rather straightforward once we know the work by Lim [Trans. Amer. Math. Soc. 360 (2008), no. 10, pp. 5089–5100] on volume entropy for graphs. As a byproduct we obtain a curvature-free version of the Collar Lemma in all dimensions.

For a classical link, Milnor defined a family of isotopy invariants, called Milnor $\overline{\mu}$-invariants. Recently, Chrisman extended Milnor $\overline{\mu}$-invariants to welded links by a topological approach. The aim of this paper is to show that Milnor $\overline{\mu}$-invariants can be extended to welded links by a combinatorial approach. The proof contains an alternative proof for the invariance of the original $\overline{\mu}$-invariants of classical links., Comment: 25 pages; v2: the title changed, Section 1 rewritten, remarks and references added; to appear in Michigan Mathematical Journal

The new L-LLC resonant bidirectional DC-DC converter (L-LLC-BDC) will produce a large resonance current and voltage inrush during the startup, posing a threat to the safe operation of the power device. Although a very high starting frequency can effectively suppress the inrush, it will also increase the output current demand of the driving ICs. This paper proposes a phase-shifting soft-start control strategy based on the current-limiting curve. Using operating mode analysis, the peak value of the resonant current is limited according to the output voltage and the phase shift angle of the switch, with the limit current curve at the startup stage drawn. By this current curve, a one-to-one correspondence between the output voltage and the phase shift angle of the switch is obtained. The phase-shifted soft-start control strategy can quickly establish the output voltage on the basis of a resonant frequency and can effectively suppress the resonance current inrush. An experimental prototype with a power of 6 kW and an input of 760 V and an output of 380 V is built. The experimental results prove the correctness and effectiveness of the soft start control strategy proposed in this paper.

During the Nazi period in Germany, an attempt was made to discern a kind of mathematics that was German as distinct from other ethnic or “racial” types of mathematics: a “Deutsche Mathematik.” While not denying the universal validity of all mathematical truths, such a “German” mathematics stressed ideology in terms of research and pedagogical styles. Because mathematics was nearly independent of anything material, it was—for the “Deutsche Mathematiker”—especially amenable to the Nazi argument that different racial psychological types exhibit different racial characters and modes of thought. This paper is a brief examination of the nature and intellectual content of “Deutsche Mathematik.”

A simulation model, and more generically, a model, is founded on its assumptions. Assurance of the model’s correctness and correct use is needed to achieve accreditation. Often the exercise of working with a specific code misunderstands the overall process, focusing the resources on the model coding and forgetting the needed resources to ensure the validation of every step of the model definition and coding. The goal of this work is to present a methodology to help in the definition and use of the assumptions in the modeling process. To do so, we present a process to conduct a simulation project, an assumptions taxonomy, and a method that simplifies working with those assumptions. We propose to extend the traditional Validation, Verification, and Accreditation processes to a process composed of eight Validation, Verification, and Accreditation phases that cover the overall life cycle of a model. Although this paper is focused on a simulation model, we can extend the proposed method to a more general modeling approach.

In this paper we consider multivariate approximation by weighted polynomials of the form w γ n ( x ) p n ( x ) w^{\gamma _n}(\mathbf {x})p_n(\mathbf {x}) , where p n p_n is a multivariate polynomial of degree at most n n , w w is a given nonnegative weight with nonempty zero set, and γ n ↑ ∞ \gamma _n\uparrow \infty . We study the question if every continuous function vanishing on the zero set of w w is a uniform limit of weighted polynomials w γ n ( x ) p n ( x ) w^{\gamma _n}(\mathbf {x})p_n(\mathbf {x}) . It turns out that for various classes of weights in order for this approximation property to hold it is necessary and sufficient that γ n = o ( n ) . \gamma _n=o(n).

The driver tries to keep the car in the center of the lane. If the car is too near the left edge, this causes the driver to make a “corrective” right turn. If the car is near the right edge, a “corrective” left turn is made. Therefore, a quantity which decreases with increasing distance ΔL from the left edge may be considered as a stimulusSR producing the reactionRR of turning to the right. A similar situation holds for the distance ΔR from the right edge. When the car is in the center of the lane, ΔL = ΔR andSR=SL, the stimuli are equal. We thus have here a situation analogous to the one studied by H. D. Landahl in his theory of psychophysical discrimination. In general a reactionRR (resp.RL) will occur only ifRR−RL≥h* (resp.RL−RR≥h*) whereh* is a threshold. Applying Landahl’s theory to this situation, we find thath* determines the distance from the edge, at which a corrective turn is made. This distance is not constant, but a function of the speedv of the car. The requirement that a corrective turn should be madebeforre the car runs off the road leads to an expression for the maximum safe speed. Because of the transcendency of the equations involved, closed solutions cannot be obtained. It is, however, shown that the expression for maximum safe speed, given in a previous paper (Bull. Math. Biophysics,21, 299–308, 1959), is a rough first approximation to the expressions found now.

In this paper, we shall establish sufficient conditions for the existence of solutions for semi-linear integrodifferential inclusions in Banach spaces with nonlocal conditions. By using suitable fixed point theorems we study the case when the multi-valued map has convex as well as nonconvex values. Rocky Mountain Journal of Mathematics

For positive functions $u\in C^{2}(\Omega) $, where $\Omega$ is an open subset of $\mathbb{R}^{n}$, the Symmetric Minimal Surface Equation (SME), is $\sum_{i=1}^{n}D_{i}\bigl(\frac{D_{i}u}{\sqrt{1+|Du|^{2}}}\bigr)=\frac{m-1}{u\sqrt{1+|Du|^{2}}}$. Geometrically, the SME expresses the fact that the ``symmetric graph'' $SG(u)$, defined by $SG(u)=\bigl\{(x,\xi)\in \Omega\times\mathbb{R}^{m}:|\xi|=u(x)\bigr\}$, is a minimal (i.e.\ zero mean curvature) hypersurface in $\Omega\times\mathbb{R}^{m}$. A function $u\in C^{1}(\Omega)$ is said to be a singular solution if $u^{-1}\{0\}\neq \emptyset$, and if $u=\lim_{j\to\infty}u_{j}$, uniformly on each compact subset of $\Omega$, where each $u_{j}$ is a positive $C^{2}(\Omega)$ solution of the SME. The present paper develops are theory of singular solutions of the SME, including existence, H\"older and Lipschitz estimates for bounded solutions, and a compactness and regularity theory. We also prove that the singular set $u^{-1}{\{0\}}$ is codimension at most 2.

Surface Green’s functions for semi-infinite systems play an important role in the design of nano-scale electronic devices. In particular, functions in multilayered periodic structures are useful for practical applications. This paper describes numerical issues associated with the computation of these functions and offers an approach to addressing these issues. The proposed approach is based on the observation that numerical errors, which can occur in the existing algorithm to compute the functions, are caused by inaccurate computation of eigenpairs. We consider an alternative approach to eigenpairs to derive an algorithm to compute the functions. Numerical experiments show that the proposed algorithm can compute functions that satisfy physical requirements.

In this paper we consider traces at initial times for functions with mixed time-space smoothness. Such results are often needed in the theory of evolution equations. Our result extends and unifies many previous results. Our main improvement is that we can allow general interpolation couples. The abstract results are applied to regularity problems for fractional evolution equations and stochastic evolution equation, where uniform trace estimates on the half-line are shown., Comment: Some typos corrected. Accepted for publication in Mathematische Nachrichten

In this paper, optimal sizing of a photovoltaic (PV) pumping system with a water storage tank (WST) is developed to meet the water demand to minimize the life cycle cost (LCC) and satisfy the probability of interrupted water (pIW) constraint considering real region data. The component sizing, including the PV resources and the WST, is determined optimally based on LCC and pIW using a new meta-heuristic method named enhanced artificial rabbits optimization (EARO) via a nonlinear inertia weight reduction strategy to overcome the premature convergence of its conventional algorithm. The WST is sized optimally regarding the lack of irradiation and inaccessibility of the pumping system so that it is able to improve the water supply reliability. The LCC for water extraction heights of 5 and 10 m is obtained at 0.2955 M$ and 0.2993 M$, respectively, and the pIW in these two scenarios is calculated as zero, which means the complete and reliable supply of the water demand of the customers using the proposed methodology based on the EARO. Also, the results demonstrated the superior performance of EARO in comparison with artificial rabbits optimization (ARO) and particle swarm optimization (PSO); these methods have supplied customers’ water demands with higher costs and lower reliability than the proposed EARO method. Also, during the sensitivity analysis, the results showed that changes in the irradiance and height of the water extraction have a considerable effect on the cost and ability to meet customer demand.

In this paper, we extend the notion of microstate free entropy to the bi-free setting. In particular, using the bi-free analogue of random matrices, microstate bi-free entropy is defined. Properties essential to an entropy theory are developed, such as the behaviour of the entropy when transformations on the left variables or on the right variables are performed. In addition, the microstate bi-free entropy is demonstrated to be additive over bi-free collections provided additional regularity assumptions are included and is computed for all bi-free central limit distributions. Moreover, an orbital version of bi-free entropy is examined which provides a tighter upper bound for the subadditivity of microstate bi-free entropy and provides an alternate characterization of bi-freeness in certain settings., Comment: (new version contains corrections, orbital bi-free entropy, and a new characterization of bi-freenness)

Nowadays, ICT play a fundamental role in education, as they are essential in all areas of knowledge at any educational stage. Specifically, in the area of mathematics, within the Primary Education stage, they are also very valid resources. This is demonstrated by the latest scientific studies. In recent times, the scientific literature has provided evidence of all this through different research studies. The aim of this paper is to analyze all those publications that deal with the teaching–learning processes of mathematics through ICT in primary education. The aim is to show the current state of the scientific literature and what elements and aspects to highlight are common to the documents analyzed. By means of the systematic literature review method, we analyzed 11 articles indexed in Scopus and the Web of Science, with the result that the use of ICT in this area is still scarce, as the volume of publications in this respect is very low. This could also indicate a prevalence of traditional methodologies associated with the teaching of mathematics that could hinder students’ acquisition of mathematical competence. However, those studies that show the use of ICT demonstrate that its use leads to an improvement in performance, motivation, and problem solving.

In this paper, we study the orbital stability of peakons and periodic peakons for a nonlinear quartic Camassa-Holm equation. We first verify that the QCHE has global peakon and periodic peakon solutions. Then by the invariants of the equation and controlling the extrema of the solution, we prove that the shapes of the peakons and periodic peakons are stable under small perturbations in the energy space.

In 1932, H. Wagner formulated the problem of the entry into water of an infinite wedge moving vertically downwards with constant speed. Among much else, Wagner noted that, in the absence of gravity, viscosity and surface tension, a similarity transformation removes time from the problem. Many other authors have considered the problem since 1932. The present paper settles a question, left open in earlier work, concerning the contact angle πβ this angle is shown, together with the wedge angle (or vertex angle) 2πα, in Figure 1(b). The question is whether the supremum.

In this paper we find necessary and sufficient conditions for the vanishing of the limit distribution for a linear combination of two real-valued additive functions. We obtain results for , where , , and are integers with , that are almost as strong as in the case of a single additive function. As an application, we resolve a conjecture of Katai.

For a fixed digraph G, the Constraint Satisfaction Problem with the template G, or CSP(G) for short, is the problem of deciding whether a given input digraph H admits a homomorphism to G. The dichotomy conjecture of Feder and Vardi states that CSP(G), for any choice of G, is solvable in polynomial time or NP-complete. This paper confirms the conjecture for a class of oriented trees called special triads. As a corollary we get the smallest known example of an oriented tree (with 33 vertices) defining an NP-complete CSP(G).

We consider the scattering of a plane wave by a locally perturbed periodic (with respect to x_1) medium. If there is no perturbation it is usually assumed that the scattered wave is quasi-periodic with the same parameter as the incident plane wave. As it is well known, one can show existence under this condition but not necessarily uniqueness. Uniqueness fails for certain incident directions (if the wavenumber is kept fixed), and it is not clear which additional condition has to be assumed in this case. In this paper we will analyze three concepts. For the Limiting Absorption Principle (LAP) we replace the refractive index n=n(x) by n(x)+iε in a layer of finite width and consider the limiting case when ε tends to zero. This will give an unsatisfactory condition. In a second approach we require continuity of the field with respect to the incident direction. This will give the same satisfactory condition as the third approach where we approximate the incident plane wave by an incident point source and let the location of the source tend to infinity.

In the present paper, the integral transform which will be called generalized Laplace transform is considered. Iteration of generalized Laplace transform and Fourier cosine transform and Fourier sine transform is generalized Glasser transform. Some identities involving these transforms and the Mellin transform and the generalized Stieltjes transform are given.

O’Grady conjectured that the Chow group of 0-cycles of the generic fiber of the universal family over the moduli space of polarized K3 surfaces of genus $g$ is cyclic. This so-called generalized Franchetta conjecture has been solved only for low genera where there is a Mukai model (precisely, when $g\leq 10$ and $g=12, 13, 16, 18, 20$), by the work of Pavic–Shen–Yin. In this paper, as a non-commutative analogue, we study the Franchetta property for families of special cubic four-folds (in the sense of Hassett) and relate it to O’Grady’s conjecture for K3 surfaces. Most notably, by using special cubic four-folds of discriminant 26, we prove O’Grady’s generalized Franchetta conjecture for $g=14$, providing the first evidence beyond Mukai models.

This paper is dedicated to the question of surjectivity of the Cauchy-Riemann operator $$\overline{\partial }$$ ∂ ¯ on spaces $${\mathcal {E}}{\mathcal {V}}(\varOmega ,E)$$ E V ( Ω , E ) of $${\mathcal {C}}^{\infty }$$ C ∞ -smooth vector-valued functions whose growth on strips along the real axis with holes K is induced by a family of continuous weights $${\mathcal {V}}$$ V . Vector-valued means that these functions have values in a locally convex Hausdorff space E over $${\mathbb {C}}$$ C . We derive a counterpart of the Grothendieck-Köthe-Silva duality $${\mathcal {O}}({\mathbb {C}}\setminus K)/{\mathcal {O}}({\mathbb {C}})\cong {\mathscr {A}}(K)$$ O ( C \ K ) / O ( C ) ≅ A ( K ) with non-empty compact $$K\subset {\mathbb {R}}$$ K ⊂ R for weighted holomorphic functions. We use this duality and splitting theory to prove the surjectivity of $$\overline{\partial }:{\mathcal {E}} {\mathcal {V}}(\varOmega ,E)\rightarrow {\mathcal {E}}{\mathcal {V}} (\varOmega ,E)$$ ∂ ¯ : E V ( Ω , E ) → E V ( Ω , E ) for certain E. This solves the smooth (holomorphic, distributional) parameter dependence problem for the Cauchy-Riemann operator on $${\mathcal {E}}{\mathcal {V}}(\varOmega ,{\mathbb {C}})$$ E V ( Ω , C ) .

where S is the Landweber-Novikov algebra. S has the added advantage of being a cocommutative Hopf algebra over Z. This paper does not remove this difficulty, but we will show that the monoid of multiplicative operations in BP*BP, (i.e. those operations which induce ring endomorphisms on BP*X for any space X)9 which we will denote by Γ{BP), has a submonoid analogous to the monoid of multiplicative operations in S.

In this paper, we extend the iterative expression for the generalized spherical functions associated with the root systems of type A previously obtained (Sawyer in Trans Am Math Soc 349(9):3569–3584, 1997; Sawyer in Q J Math Oxf Ser (2) 50(197):71–86, 1999) beyond regular elements. We also provide a similar expression in the corresponding flat case. From there, we derive a Laplace-type representation for the generalized spherical functions associated with the root systems of type A in the Dunkl setting as well as in the trigonometric Dunkl setting. This representation leads us to describe precisely the support of the generalized Abel transform. Thanks to a recent result of Gallardo and Rejeb (Support properties of the intertwining and the mean value operators in Dunkls analysis. Preprint [hal01331693], pp 1–10, 2016) and Rejeb (Harmonic and subharmonic functions associated with root systems. Mathematics, Universite Francois-Rabelais de Tours, Universite de Tunis El Manar, 2015), which allows us to give the support for the Dunkl intertwining operator.

This paper is devoted to wavelet analysis on adele ring $\bA$ and the theory of pseudo-differential operators. We develop the technique which gives the possibility to generalize finite-dimensional results of wavelet analysis to the case of adeles $\bA$ by using infinite tensor products of Hilbert spaces. The adele ring is roughly speaking a subring of the direct product of all possible ($p$-adic and Archimedean) completions $\bQ_p$ of the field of rational numbers $\bQ$ with some conditions at infinity. Using our technique, we prove that $L^2(\bA)=\otimes_{e,p\in\{\infty,2,3,5,...}}L^2({\bQ}_{p})$ is the infinite tensor product of the spaces $L^2({\bQ}_{p})$ with a stabilization $e=(e_p)_p$, where $e_p(x)=\Omega(|x|_p)\in L^2({\bQ}_{p})$, and $\Omega$ is a characteristic function of the unit interval $[0,\,1]$, $\bQ_p$ is the field of $p$-adic numbers, $p=2,3,5,...$; $\bQ_\infty=\bR$. This description allows us to construct an infinite family of Haar wavelet bases on $L^2(\bA)$ which can be obtained by shifts and multi-delations. The adelic multiresolution analysis (MRA) in $L^2(\bA)$ is also constructed. In the framework of this MRA another infinite family of Haar wavelet bases is constructed. We introduce the adelic Lizorkin spaces of test functions and distributions and give the characterization of these spaces in terms of wavelet functions. One class of pseudo-differential operators (including the fractional operator) is studied on the Lizorkin spaces. A criterion for an adelic wavelet function to be an eigenfunction for a pseudo-differential operator is derived. We prove that any wavelet function is an eigenfunction of the fractional operator. These results allow one to create the necessary prerequisites for intensive using of adelic wavelet bases and pseudo-differential operators in applications., Comment: 45 pages

In this paper we study the homogenization of an eigenvalue problem for a cooperative system of weakly coupled elliptic partial differential equations, called the neutronic multigroup diffusion model, in a periodic heterogeneous domain. Such a model is used for studying the criticality of nuclear reactor cores. In a recent work in collaboration with Grégoire Allaire, it is proved that, under a symmetry assumption, the first eigenvector of the multigroup system in the periodicity cell controls the oscillatory behaviour of the solutions, whereas the global trend is asymptotically given by a homogenized diffusion eigenvalue problem. It is shown here that when this symmetry condition is not fulfilled, the asymptotic behaviour of the neutron flux, corresponding to the first eigenvector of the multigroup system, is dramatically different. This result enables to consider new types of geometrical configurations in practical nuclear reactor core computations.

This paper extends the Wittrick-Williams (W-W) algorithm for hybrid dynamic stiffness (DS) models connecting any combinations of line and point nodes. The principal novelties lie in the development of both the DS formulation and the solution technique in a sufficiently systematic and general manner. The parent structure is considered to be in the form of two dimensional DS elements with line nodes, which can be connected to rigid/spring point supports/connections, rod/beam point supports/connections, and point connections to substructures. This is achieved by proposing a direct constrain method in a strong form which makes the modeling process straightforward. For the solution technique, the W-W algorithm is extended for all of the above hybrid DS models. No matrix inversion is needed in the proposed extension, making the algorithm numerically stable, especially for complex built-up structures. A mathematical proof is provided for the extended W-W algorithm. The proposed DS formulation and the extended W-W algorithm are validated by the FE results computed by ANSYS. This work significantly extends the application scope of the DS formulation and the W-W algorithm in a methodical and reliable manner, providing a powerful eigenvalue analysis tool for beam-plate built-up structures.

The Moreau envelopes of nonconvex functions on a real Hilbert space have points of nondifferentiability called singularities. For the first time in an infinite-dimensional space, the propagation of singularities along intrinsic characteristic curves $${\varvec{x}}(t)$$ x ( t ) is studied. The properties of the intrinsic characteristics are investigated in some detail. It is proved that singularities propagate along intrinsic characteristics not only locally but globally in t. Actually, this paper distinguishes between “singularities” and “strong singularities,” two concepts that agree for distance functions but disagree for Moreau envelopes, in general. Along intrinsic characteristics, propagating singularities instantaneously transform into strong singularities. Concerning the distance function to a closed nonempty set E, it is demonstrated that the singular set and $$\complement E$$ ∁ E are homotopy equivalent provided E satisfies a certain condition which is weaker than the boundedness of $$\complement E$$ ∁ E . The notion of intrinsic characteristics was introduced by Cannarsa and Cheng (Calc Var Part Differ Equ 56, 2017).

In this paper, we study a finite capacity queue where the arrival process is a special case of the discrete time Markov modulated Poisson process, the service times are generally distributed, and the server takes repeated vacations when the system is empty. The buffer acceptance strategy is based on a generalized push-out scheme: when the buffer is full, an arriving customer pushes out the Nth customer in the queue, where N takes values between 2 and the capacity of the system, and the arriving customer joins the end of the queue. Such a strategy is important when, as well as short waiting times for served customers, the time a pushed-out customer occupies a buffer space is also an important performance measure. The Laplace transform of the waiting time of a served customer is determined. Numerical examples show the influence of the bustiness of the input process and also the trade-off between the average waiting time of served customers and the occupancy of the buffer space of pushed-out customers.

This is the first of a series of three papers devoted to the regularity of solutions of elliptic problems on nonsmooth domains in ℝ3. The present paper introduces various weighted spaces and countably weighted spaces in the neighbourhood of edges and vertices of polyhedral domains, and it concentrates on exploring the structure of these spaces, such as the embeddings of weighted Sobolev spaces, the relation between weighted Sobolev spaces and weighted continuous function spaces, and the relations between the weighted Sobolev spaces and countably weighted Sobolev spaces in Cartesian coordinates and in the spherical and cylindrical coordinates. These well-defined spaces are the foundation for the comprehensive study of the regularity theory of elliptic problems with piecewise analytic data in ℝ3, which are essential for the design of effective computation and the analysis of the h – p version of the finite element method for solving elliptic problems in three-dimensional nonsmooth domains arising from mechanics and engineering.

This paper focuses on the spherical fixed point set of a circle action on an ALE space endowed with Kronheimer's hyperkaehler metric. The induced metric on the sphere is described by using the algebraic geometry of rational curves on algebraic surfaces, in particular the lines on a cubic., Dedicated to the memory of Michael Atiyah

Let k be a field of characteristic zero. We prove that the derivation D = @=@x + (y s + px)(@=@y), where s 2, 06 p2 k, of the polynomial ring k(x;y) is simple. 1. Introduction. Throughout the paper k is a field of characteristic zero. Assume that d is a derivation of a commutative k-algebra R. We say that d is simple if R has no d-invariant ideals other than 0 and R. Simple derivations are useful for constructions of simple noncommutative rings which are not fields. It is well known ((2)) that if R(t;d) is the Ore

In this paper we obtain the Plancherel formula for the spaces of L 2 -sections of line bundles over the complex projective hyperboloids G=H withGD U.p;qIC/ andHD U.1IC/ U.p 1;qIC/. The Plancherel formula is given in an explicit form by means of spherical distributions associated with a character of the subgroupH . We obtain the Plancherel formula by a special method which is also suitable for other problems, for example, for quantization in the spirit of Berezin. © 2000 Editions scientifiques et medicales Elsevier SAS Keywords: Plancherel formula, Spherical distributions, Complex hyperbolic spaces In this paper we obtain the Plancherel formula for the spaces of L 2 -sections of line bundles over the complex projective hyperboloids G=H with GD U.p;qIC/ and H D U.1IC/ U.p 1;qIC/, i.e. we present the decomposition of L 2 into irreducible represen- tations of the group G of class . In order to leave aside the well-known case of a hyperboloid with compact stabilizer subgroup, see (14), we assumep>1 ;q >0. The Plancherel formula is given in an explicit form by means of spherical distributions associated with a character of the subgroup H. We obtain the Plancherel formula by Molchanov's method, see (9). Namely, we follow the detailed scheme in (1), Sections 4, 7. This method deals with the spectral resolution of the radial part of the Laplace operator. The essential step is setting the boundary conditions at certain special points. Those conditions are prescribed by the behaviour of spherical distributions. Finally, it is necessary to perform various analytic continuations. This method is also suitable for other problems, for example, for quantization in the spirit of Berezin, namely, for the decomposition of the Berezin form. It is therefore why this method has to be preferred to the existing methods, described in (3). We use our results from (13). There we define -spherical distributions, study their asymptotic behaviour and express them by means of hypergeometric functions. We describe the irreducible unitary representations of the group G ,o f class associated with an isotropic cone. We give constructions for the Fourier and Poisson transform, define intertwining operators and diagonalize them. Some of those results are presented in Section 1.

The estimation of economies of scope between research and teaching has been the object of a large literature in economics of education and efficiency analysis, with parametric and non-parametric specifications. The paper contributes to the literature by building a pan-European dataset that integrates official statistics on higher education at country level with bibliometric indicators. The dataset allows a breakdown by scientific and educational field, accounting for the heterogeneity among disciplines. We applied a technique which has not been used for the efficiency estimation of economies of scope in higher education, namely seemingly unrelated regression (SUR) applied to separate input–output equations describing the production of education and research. We found confirmation for economies of scope in some fields and with some specifications, or no relation between the equations. In no case did we find diseconomies of scope between teaching and research.