Analysis (Mathematics)

Este artículo presenta una formulación para la solución de la ecuación de consolidación unidimensional en suelos estratificados utilizando el método de series de Fourier. Se considera el caso de dos capas arcillosas. Se detallan las condiciones de contorno en los extremos del dominio y en la interfaz entre las capas. Se exploran las dificultades asociadas con la determinación de los valores propios y la ortogonalidad, proporcionando una base teórica sólida para el análisis de la consolidación en suelos estratificados

Este manual recoge los contenidos de las asignaturas Matemáticas Empresariales y Matemáticas Económico-empresariales (plan 2000) que se imparten en la Universitat de València. En cada tema, se exponen los resultados teóricos necesarios acompañados de ejercicios resueltos a modo de ejemplo y destacando los hechos más relevantes que el alumno debe recordar a la hora de resolver problemas. Se incluye también la demostración de algunos teoremas. Más concretamente, hemos seleccionado aquellas que consideramos que -sin exceder el nivel exigible a los alumnos-pueden ayudarles a familiarizarse con los conceptos que va a manejar. Así mismo, cada tema termina con una colección de ejercicios propuestos. En todos los temas hemos intentado mostrar la conexión de las técnicas expuestas con la teoría económica y sus aplicaciones a la empresa. Para ello hemos incluido numerosos ejemplos con enunciado económico, los cuales no han de entenderse como aplicaciones realistas de la teoría, sino como una forma de que el alumno entienda el uso que se dará en otras asignaturas de su carrera a los conceptos estudiados. Queremos agradecer a nuestros compañeros el apoyo y la ayuda que nos han prestado, especialmente a Manuel Mocholí, que nos animó a emprender el trabajo.

Quasi-lattices are introduced in terms of 'join' and 'meet' operations. It is observed that quasi-lattices become lattices when these operations are associative and when these operations satisfy 'modularity' conditions. A fundamental theorem of homomorphism proved in this article states that a quasi-lattice can be mapped onto a lattice when some conditions are satisfied.

For an algebraic structure sJ = (A, F, R) or type r and a set S of open formulas of the first order language L(T) we introduce the concept of S-closed subsets of s/. The set 'tfs (.c/) of all E-closed subsets forms a complete lattice. Algebraic structures sj, 8$ of type r are called E-isomorphic if 'rfsf.c/) = ^(Sl). Examples of such S-closed subsets are e.g. subalgebras of an algebra, ideals of a ring, ideals of a lattice, convex subsets of an ordered or quasiordered set etc. We study E-isomorphic algebraic structures in dependence on the properties of E.

Abs tract Over the last thirty years much progress has been made in the investigation of the lattice of uniformities on a set X. In particular, P elant, Reiterman, Rodl and Simon have published several articles concerning anti-atoms and complements in this lattice. The aim of this dissertation is to begin a similar investigation into the lattice of quasi-uniformi t ies 8 (X) on a set X. It starts off with a summary of results obtained for the lattice of topologies on X, which, having been studied in great detail in the past, is intended as an example as to what may be achieved with 8(X). An exposit ion of the lattice of uniformities is then given. \Ne conclude by commencing an investigation into the lattice of quasi-uniformiti es on X. Where possible, results obtained for the lattice of uniformities are generalized to 8(X) , and some original results for 8 (X) are also presented. First and foremost , I would like to thank my supervisor, Prof. H.-P. Kunzi , for all his help and support over the last year and a half. I have greatly benefitted from his expertise in this area of mathematics, and I appreciate the countless times that he has pointed me in the right direction. In addition to this, I would like to thauk the entire teaching staff in the Department of Mathematics and Applied Mathematics at the University of Cape Town. From as early as the first and second years of my bachelors degree, their encouragment and love for the subject inspired me to do my very best. In my third and fourth years of study their enthusiasm and excellent teaching abilities continued to inspire me, and made an already interresting subject that much more enjoyable. I would also like to thank Assoc. Prof. B. D. Hahn, who t the last moment made available to me a scholarship for my honours degree without which I would not have been here today. Last but not least, I would also like to thank the RF for my Prestigious Scholarhip, which made st dying towards my masters degree possible.

In Huang and Weng (2004), Huang and Weng introduced pooling spaces, and constructed pooling designs from a pooling space. In this paper, we introduce the concept of pooling semilattices and prove that a pooling semilattice is a pooling space, then show how to construct pooling designs from a pooling semilattice. Moreover, we give many examples of pooling semilattices and thus obtain the corresponding pooling designs.

In this paper, we provide an alternative description of the duality result for distributive lattices and coherent locales using ultraposet. In particular, we show that there are fully faithful embeddings from the opposite of the category of distributive lattices into the category of ultraposets with ultrafunctors, and from the category of coherent locales into the category of ultraposets with left ultrafunctors. We also define the notion of zero-dimensional ultraposets, which characterises the essential image of these embeddings.

We lay down the foundations for a pointfree theory of Pervin spaces. A Pervin space is a set equipped with a bounded sublattice of its powerset, and it is known that these objects characterize those quasi-uniform spaces that are transitive and totally bounded. The pointfree notion of a Pervin space, which we call Frith frame, consists of a frame equipped with a generating bounded sublattice. In this paper we introduce and study the category of Frith frames and show that the classical dual adjunction between topological spaces and frames extends to a dual adjunction between Pervin spaces and Frith frames. Unlike what happens for Pervin spaces, we do not have an equivalence between the categories of transitive and totally bounded quasi-uniform frames and of Frith frames, but we show that the latter is a full coreflective subcategory of the former. We also explore the notion of completeness of Frith frames inherited from quasi-uniform frames, providing a characterization of those Frith frames that are complete and a description of the completion of an arbitrary Frith frame.

Nets, useful topological tools, used to generalize certain concepts that may only be general enough in the context of metric spaces. In this work we introduce this concept in an S-poset, a poset with an action of a posemigroup S on it which is a very useful structure in computer sciences and interesting for mathematicians, and give the concept of S-net. Using S-nets and its convergency we also give some characterizations of separated S-posets. Also, introducing the net-closure operators, we investigate the counterparts of topological separation axioms on S-posets and study their relation to separated S-posets.

In this paper, we characterize various local forms of T4 constant filter convergence spaces and investigate the relationships among them as well as showing that the full subcategories of the category of constant filter convergence spaces consisting of local T4 constant filter convergence spaces that are hereditary. Furthermore, we examine the relationship between local T4 and general T4 constant filter convergence spaces. Finally, we present Urysohn's lemma and Tietze extension theorem for constant filter convergence spaces.

Considered convergence and limit for funcoids (a generalization of proximity spaces). I also have defined (generalized) limit for arbitrary (not necessarily continuous) functions under certain conditions. This article is a part of my Algebraic General Topology research.

They are studied in details properties of filters on lattices, filters on posets, and certain generalizations thereof. Also it's done some more general lattice theory research. There are posed several open problems. Detailed study of filters is required for my ongoing research which will be published as "Algebraic General Topology" series.

Quasi-lattices are introduced in terms of 'join' and 'meet' operations. It is observed that quasi-lattices become lattices when these operations are associative and when these operations satisfy 'modularity' conditions. A fundamental theorem of homomorphism proved in this article states that a quasi-lattice can be mapped onto a lattice when some conditions are satisfied.

Introduced several new axiomatic systems, that are not less general than group theory, and discovered discontinuous analysis. In this work I introduce and study in details the concepts of funcoids which generalize proximity spaces and reloids which generalize uniform spaces, and generalizations thereof. The concept of funcoid is generalized concept of proximity, the concept of reloid is cleared from superfluous details (generalized) concept of uniformity. Also funcoids and reloids are generalizations of binary relations whose domains and ranges are filters (instead of sets). Also funcoids and reloids can be considered as a generalization of (oriented) graphs, this provides us with a common generalization of calculus and discrete mathematics. I consider (generalized) limit of arbitrary (discontinuous) function, defined in terms of funcoids. Definition of generalized limit makes it obvious to define such things as derivative of an arbitrary function, integral of an arbitrary function, etc. It is given a definition of non-dif\-fe\-re\-nti\-able solution of a (partial) differential equation. It's raised the question how do such solutions ``look like'' starting a possible big future research program. The generalized solution of one simple example differential equation is also considered. The generalized derivatives and integrals are linear operators. For example $\int_a^b f(x)dx - \int_a^b f(x)dx = 0$ is defined and true for \emph{every} function. The concept of continuity is defined by an algebraic formula (instead of old messy epsilon-delta notation) for arbitrary morphisms (including funcoids and reloids) of a partially ordered category. In one formula continuity, proximity continuity, and uniform continuity are generalized. Also I define connectedness for funcoids and reloids. Then I consider generalizations of funcoids: pointfree funcoids and generalization of pointfree funcoids: staroids and multifuncoids. Also I define several kinds of products of funcoids and other morphisms. I define \emph{space} as an element of an ordered semigroup action, that is a semigroup action conforming to a partial order. Topological spaces, uniform spaces, proximity spaces, (directed) graphs, metric spaces, etc.\ all are spaces. It can be further generalized to ordered precategory actions (that I call interspaces). I build basic general topology (continuity, limit, openness, closedness, hausdorffness, compactness, etc.) in an arbitrary space. Now general topology is an algebraic theory. Before going to topology, this book studies properties of co-brouwerian lattices and filters.

Introduced several new axiomatic systems, that are not less general than group theory, and discovered discontinuous analysis. In this work I introduce and study in details the concepts of funcoids which generalize proximity spaces and reloids which generalize uniform spaces, and generalizations thereof. The concept of funcoid is generalized concept of proximity, the concept of reloid is cleared from superfluous details (generalized) concept of uniformity. Also funcoids and reloids are generalizations of binary relations whose domains and ranges are filters (instead of sets). Also funcoids and reloids can be considered as a generalization of (oriented) graphs, this provides us with a common generalization of calculus and discrete mathematics. I consider (generalized) limit of arbitrary (discontinuous) function, defined in terms of funcoids. Definition of generalized limit makes it obvious to define such things as derivative of an arbitrary function, integral of an arbitrary function, etc. It is given a definition of non-dif\-fe\-re\-nti\-able solution of a (partial) differential equation. It's raised the question how do such solutions ``look like'' starting a possible big future research program. The generalized solution of one simple example differential equation is also considered. The generalized derivatives and integrals are linear operators. For example $\int_a^b f(x)dx - \int_a^b f(x)dx = 0$ is defined and true for \emph{every} function. The concept of continuity is defined by an algebraic formula (instead of old messy epsilon-delta notation) for arbitrary morphisms (including funcoids and reloids) of a partially ordered category. In one formula continuity, proximity continuity, and uniform continuity are generalized. Also I define connectedness for funcoids and reloids. Then I consider generalizations of funcoids: pointfree funcoids and generalization of pointfree funcoids: staroids and multifuncoids. Also I define several kinds of products of funcoids and other morphisms. I define \emph{space} as an element of an ordered semigroup action, that is a semigroup action conforming to a partial order. Topological spaces, uniform spaces, proximity spaces, (directed) graphs, metric spaces, etc.\ all are spaces. It can be further generalized to ordered precategory actions (that I call interspaces). I build basic general topology (continuity, limit, openness, closedness, hausdorffness, compactness, etc.) in an arbitrary space. Now general topology is an algebraic theory. Before going to topology, this book studies properties of co-brouwerian lattices and filters.

Bazându-mă pe proprietatea remarcabilă a vectorului lui Darboux de a fi perpendicular pe normală, definesc un nou triedru asociat curbelor din spațiu și demonstrez că și acest triedru satisface formulele lui Frenet. Spre deosebire de lucrarea anterioară ([2]), unde am folosit pentru simplitate forma trigonometrică a formulelor lui Frenet, în această lucrare construiesc o demonstrație bazată doar pe curbură și torsiune, respectiv, pe darbuzian și lancretian.

Tabla 1.1. Valores de los números complejos de la Figura 1.2. Losángulos están en radianes, con aproximación a dos decimales (180 • = π 3,14) y se miden respecto al eje x. Losángulos notables se expresan en términos de π. Una propiedad muy importante de un número complejo en su forma polar es que si el argumento se modifica de la forma φ → φ + 2nπ, donde n es un número entero (n ∈ Z), su valor no cambia. 1 Esto es lógico porque es análogo a rotar un vector un número entero de vueltas en dirección horaria (n < 0) o antihoraria (n > 0). Note usted que después de dar una, dos, o más vueltas hacia la izquierda o hacia la derecha, seguiría mirando en la misma dirección inicial. Matemáticamente, es fácil darse cuenta que z no cambia z = |z|e iφ = |z|e i(φ+2nπ) = |z|e iφ e 2inπ = z cos(2nπ) + i sin(2nπ) = z , (1.13) debido a que cos(2nπ) = 1 y sin(2nπ) = 0. Notemos que si n no es entero, el número complejo cambia de valor, como es de esperar, porque su dirección cambia necesariamente. Este concepto será de suma importancia cuando se definan en futuras secciones los conceptos de funciones univaluadas y multivaluadas. 1 Usaremos la notación Z para denotar el conjunto de los números enteros. 1.4. Ecuaciones algebraicas y desigualdades 15 Ejemplos de la sección 1.3 1. Expresemos z 1 y z 2 de la forma cartesiana z = x + iy.

In their recent paper on posets with a pseudocomplementation denoted by * the first and the third author introduced the concept of a *-ideal. This concept is in fact an extension of a similar concept introduced in distributive pseudocomplemented lattices and semilattices by several authors, see References. Now we apply this concept of a c-ideal (dually, c-filter) to complemented posets where the complementation need neither be antitone nor an involution, but still satisfies some weak conditions. We show when an ideal or filter in such a poset is a c-ideal or c-filter, and we prove basic properties of them. Finally, we prove the so-called separation theorems for c-ideals. The text is illustrated by several examples.

We show that metrizability and bounded tightness are actually equivalent for a large class G of locally convex spaces including (LF)-spaces, (DF)-spaces, the space of distributions D (Ω), etc. A consequence of this fact is that for X ∈ G the bounded tightness for the weak topology of X is equivalent to the following one: X is linearly homeomorphic to a subspace of ω := R N. This nicely supplements very recent results of Cascales and Raja. Moreover, we show that a metric space X is separable if the space C p (X) has bounded tightness.

L'accès aux archives de la revue « Annales mathématiques Blaise Pascal » (http:// math.univ-bpclermont.fr/ambp/) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

In answer to Jarchow’s 1981 text, we recently characterized when $C_{\textrm{c}}(X)$ is a $df$-space, finding along the way attractive analytic characterizations of when the Tychonov space $X$ is pseudocompact. Analogues now reveal how exquisitely Warner boundedness lies between these two notions. To illustrate, $X$ is pseudocompact, $X$ is Warner bounded or $C_{\textrm{c}}(X)$ is a $df$-space if and only if for each sequence $(\mu_{n})_{n}\subset C_{\textrm{c}}(X)&#39;$ there exists a sequence $(\varepsilon_{n})_{n}\subset(0,1]$ such that $(\varepsilon_{n}\mu_{n})_{n}$ is weakly bounded, is strongly bounded or is equicontinuous, respectively. Our characterizations and proofs add to and simplify Warner’s.AMS 2000 Mathematics subject classification: Primary 46A08; 46A30; 54C35

A new characterization of spherical completeness of non-archimedean valued fields is obtained. INTRODUCTION Throughout I16 denotes a non-archimedean valued field which is complete under the metric induced by the non-trivial valuation 1 I. ll6 is said to be spherically complete [2] if the intersection of every shrinking sequence of balls in 06 is non-empty. Clearly spherical completeness implies completeness; the converse fails, cf. also [2]. From Ingleton's main result of [2] it follows that for a Knormed space E, i.e. a non-archimedean normed space over Dd, the Hahn-Banach theorem concerning the extension of linear functionals over E is true iff Dd is spherically complete. This partially explains the importance of the spherical completeness in non-archimedean functional analysis. Another characterizations of spherical completeness of K can be found in [5], Theorem 4.15. Developing some ideas of [3] to the non-archimedean case we prove the following. Theorem. The following conditions on Q6 are equivalent. (i) K is spherically complete.

DEDICATED TO THE MEMORY OF GIAN-CARLO ROTA, AMICO DI MATEMATICA Locally convex Baire spaces have poor permanence properties, as demonstrated by Valdivia's non-Baire product of two Baire spaces, which also proves that Baire is not a three-space property. The opposite is true of Baire-like (BL) and others in a long list of weaker space properties whose three-space status is known. We add semi-Baire-like (sBL) to the list. It has long been known that quasi-Baire (QB) is a three-space property, since a space is QB if and only if it is barrelled and non-S σ , and the latter two are three-space properties. Since BL spaces are just those barrelled spaces that are sBL, the result would be similarly immediate for BL if sBL were a three-space property. Such a proof is impossible, for we show that sBL is not a three-space property, and much more: in the extended context, our results answer with optimal efficiency all remaining 631 questions of the form: "if F has property a and E/F has property b, then must the third space E have property c?"

Representation and reasoning about dynamic spatial phenomena requires at its foundation a formalism of spatial change. This paper extends our understanding of topological change, by providing a classification and analysis of events associated with changes in topological structures of spatial areal objects as they evolve through time. Tree structures are employed to represent topological relationships between regions and holes of areal objects. Basic and complex changes are specified using structure-preserving mappings between trees. Further, the paper constructs a normal form, and proves that it is the 'simplest' form that can represent all the changes under consideration.

A plane poset is a finite set with two partial orders, satisfying a certain incompatibility condition. The set PP of isoclasses of plane posets owns two products, and an infinitesimal Hopf algebra structure is defined on the vector space H PP generated by PP, using the notion of biideals of plane posets. We here define a partial order on PP, making it isomorphic to the set of partitions with the weak Bruhat order. We prove that this order is compatible with both products of PP; moreover, it encodes a non degenerate Hopf pairing on the infinitesimal Hopf algebra H PP .

Bazându-mȃ pe proprietatea remarcabilȃ a vectorului lui Darboux de a fi perpendicular pe normalȃ, definesc un nou triedru asociat curbelor din spat , iu s , i demonstrez cȃ s , i acest triedru satisface formulele lui Frenet. Spre deosebire de lucrȃrile anterioare, unde am folosit pentru simplitate forma trigonometricȃ a formulelor lui Frenet,în aceastȃ lucrare construiesc o demonstrat , ie bazatȃ doar pe curburȃ s , i torsiune, respectiv, pe darbuzian s , i lancretian.

We characterize the convergence of fuzzy sets in the supremum metric given by the supremum of the Hausdorff distances of the α-cuts of the fuzzy sets. We do it by dividing this metric into its lower and upper quasipseudometric parts. This characterization is given in the more general context with no assumption on the fuzzy sets. Furthermore, motivated from the theory of Convex Analysis, we also provide some results about the behaviour of the convergence in the supremum metric with respect to maximizers.

Proglacial rivers have been shown to have distinctive silicon (Si) isotope compositions, providing new insights into the mechanisms controlling Si cycling in the subglacial environment and suggesting terrestrial Si isotope exports may have varied between glacial and interglacial periods. However, Si isotope data are currently limited to a small number of glacial systems in the northern hemisphere, and it is unclear how compositions might vary across a spectrum of glacial influence. Using Chilean Patagonia as a unique natural laboratory, we present Si isotope compositions of 0.45 μm filtered (fSi), 0.02 μm filtered (DSi), and reactive amorphous (ASi) fractions from 40 river catchments with variable glacial cover and explore the key controls on Si cycling. The 0.45 μm filtered glacier-fed river samples displayed isotopically light compositions and a positive linear correlation with upstream glacial cover. This relationship was controlled by the inclusion of an isotopically light collo...

Centrifugal fan is a mechanical device working on the principle of centrifugal pump. When working, propeller sucks air along the axis, the pressure at the fan center will be small. The air will move from high pressure region to where the pressure is low. In other words, the air will receive additional centrifugal forces. The appearance of centrifugal fan has brought us many benefits such as basement ventilation systems or where ventilation fans enable to be directly established. Hence, the study of the performance characteristics of centrifugal fan is currently a matter concern, from which the improvement of performance can be applied to the fan. In this paper, a model simulating the performance characteristics of centrifugal fan was done on snappyHexMesh ultility with mainly hexahedron girds. Therefore, the results of the performance characteristics of centrifugal fan use k – omega SST is compared with experimental data. The results obtained from automatic meshing snappyHexmesh ult...

In this paper a perturbed system of exponents with a unit, whose phase is a linear function depending on a real parameter is considered. The necessary and sufficient conditions for the parameter for the basis properties (completeness, minimality and basicity) of this system are found in the subspace of Morrey space in which continuous functions are dense.

First I define a product of two funcoids. Then I define multidimensional funcoids (or multifuncoids) as a generalization of funcoids. Using multifuncoids I define a product of an arbitrary (possibly infinite) family of funcoids. 1 Draft status It is a rough partial draft. 2