Duality Theory

We study the space of L 2 harmonic forms on complete manifolds with metrics of fibred boundary or fibred cusp type. These metrics generalize the geometric structures at infinity of several different well-known classes of metrics, including asymptotically locally Euclidean manifolds, the (known types of) gravitational instantons, and also Poincaré metrics on Q-rank 1 ends of locally symmetric spaces and on the complements of smooth divisors in Kähler manifolds. The answer in all cases is given in terms of intersection cohomology of a stratified compactification of the manifold. The L 2 signature formula implied by our result is closely related to the one proved by Dai [25] and more generally by Vaillant [67], and identifies Dai's τ-invariant directly in terms of intersection cohomology of differing perversities. This work is also closely related to a recent paper of Carron [12] and the forthcoming paper of Cheeger and Dai [17]. We apply our results to a number of examples, gravitational instantons among them, arising in predictions about L 2 harmonic forms in duality theories in string theory.

There is considerable debate as to the determinants of the human resource policies of human resource management: do they reflect national institutional or cultural realities, emerging common global practices, parent country effects or the dual effects of transnational and national realities? We use an extensive international database to explore these differences, assessing variations in a range of human resource practices. We find new evidence of national differences in the manner in which indigenous firms manage their people, but also evidence of a similarity in practice amongst multinational corporations. In other words, multinational corporations tend to manage their human resources in ways that are distinct from those of their host country; at the same time, country of origin effects seem relatively weak. Whilst there is some evidence of common global practices, sufficient diversity in practice persists to suggest that duality theories may provide the most appropriate explanation.

THIS IS NATURE SIGNALING THE END OF DUALITY 
THIS IS HUGE - CHANGE THE ENTIRETY OF CREATION - NO DUALITY ANYWHERE.
IT IS VERY CLEARLY A PREDETERMINED ADVANCEMENT OF HUMAN CONSCIOUSNESS - THIS BUBBLE IS TOO WELL DESIGNED - EUPHORIA CANCELS KARMA

Most of the literature related to the measurement of economic efficiency has based its analysis either on parametric or on non-parametric frontier methods. The choice of estimation method has been an issue of debate, with some researchers preferring the parametric and others the non-parametric approach. The aim of this paper is to provide a critical and detailed review of both core frontier methods. In our opinion, no approach is strictly preferable to any other. Moreover, a careful consideration of their main advantages and disadvantages, of the data set utilized, and of the intrinsic characteristics of the framework under analysis will help us in the correct implementation of these techniques. Recent developments in frontier techniques and economic efficiency measurement such as Bayesian techniques, bootstrapping, duality theory and the analysis of sampling asymptotic properties are also considered in this paper.

Wuthering Heights is recognized as the masterpiece of Emily Brontë, not only by the way she demonstrates how love and hate can be closely related but also by the particular way she organizes the elements of the book through pairs and using parallel events. Through this organization, Brontë can show the relationship between two characters and why they love or hate each other, the influence of the two main settings in each character, and why the opposite themes are significant for the development of the story. The main idea of Brontë behind this arrangement is that of making contrasts and show similarities among the different elements and characters.

Human-created every Believe is philosophy.
Philosophy comes from vision and is applied on space and time. Every philosophy is born out of vision. Every purpose is defined by vision and on the basis of vision, the explanation of "I" and "we" are decided. According to the ancient Indian knowledge system, vision was divided into four philosophy groups(three vision and forth no vision), which are also known as philosophy groups. Nature philosophy school (republic/tribal) comes with the vision of equality. "I" comes from "we" and without "we", "I" has no individual identity. Duality philosophy school (dictatorship) comes with the vision of dictatorship. "We" comes from "I" and the whole world exists for me because I exist. So the existence of "I" is the most important aspect. Capitalist philosophy school (civilized) comes with two types of systems-atheist and theist.

तानाशाही दर्शन के आधार पर बनी व्यवस्था वैष्णव दर्शन ,द्वैत दर्शन के नाम से जानी गई ।
तानाशाही व्यवस्था जमीदारी व्यवस्था,सामंतवाद ,भूमियार ,व नौकरशाही जैसी व्यवस्था को कहते है ।
इस दर्शन मे जल जंगल जमीन जैसी प्रकर्तिक संसाधनों पर राजा या नौकेरशाह  का अधिकार था । यहा भी प्रकृतिक संसाधनों को ख़रीदा या बेच नही जा सकता था ।

This paper presents three results that the author obtained in his doctoral thesis (Kümmerle, 2018a) where he investigated the topic from the viewpoints of institutionalization and the circulation of knowledge.
These are: 1. While mathematical colloquia (danwakai) at the Imperial Universities in Kyōto and Tōhoku were born out of necessity, they stimulated research and helped create distinctive research traditions. In Tōkyō, where mathematicians could present at the regular meetings of the Mathematico-Physical Society, a colloquium relevant for mathematical research was created only in 1920. 2. With more than 90%, the ratio of non-high school graduates among all students at Tōhoku Imperial University specializing in mathematics was, at least in the 1910s, much higher than the literature has suggested. "Practical mathematics" was embedded in the curriculum, topics in the seminar classes went beyond pure mathematics, and many students of mathematics chose topics of applied mathematics when progressing to graduate school. The case of Iwatsuki Toranosuke, who became one of the founders of the school of "wave geometry", can be seen as representative of this atmosphere. 3. An analysis of the chair system can explain why the focus on pure mathematics established by Fujisawa Rikitarō at Tōkyō Imperial University persisted. After the formal requirement to teach applied mathematics was passed on to the department of physics in the first years of the 20 th century, Fujisawa and the other professors of mathematics, coherent with the principle of academic self-governance, did not follow other departments in establishing new chairs with clearer tasks. When they finally obtained one more chair in 1920, it was dedicated to mathematics in general. This provided the basis for continuing to ignore applications, with the exception of the lecture on probability and statistics.
Moreover, based on experiences made during research on Tannaka Tadao's paper on the duality of non-Abelian groups (Tannaka, 1938), this paper proposes three problems for further research: 1. Contextualize the economic and institutional situation of Japanese mathematicians. 2. Investigate both the reception of research results abroad and how Japanese mathematicians anticipated the reception before publication. 3. Pay close attention to Japanese-language papers and include them with translations into English in edited volumes.

There is considerable debate as to the determinants of the human resource policies of human resource management: do they reflect national institutional or cultural realities, emerging common global practices, parent country effects or the dual effects of transnational and national realities? We use an extensive international database to explore these differences, assessing variations in a range of human resource practices. We find new evidence of national differences in the manner in which indigenous firms manage their people, but also evidence of a similarity in practice amongst multinational corporations. In other words, multinational corporations tend to manage their human resources in ways that are distinct from those of their host country; at the same time, country of origin effects seem relatively weak. Whilst there is some evidence of common global practices, sufficient diversity in practice persists to suggest that duality theories may provide the most appropriate explanation.

Every day a large number of problems are studied and analyzed where modeling in the form of networks is a way of being more efficient in the search for efficient results for companies, organizations, associations and even in problems of particular interest, at each moment gradually the number of Study requirements of this type of case are becoming more frequent, this research document tries to show an alternative way of finding a solution to problems that can be very complicated, since they can exponentially increase the modeling as a whole of equations and feasible spaces hence the importance of remembering interesting linear programming algorithms as a source of inspiration for the state of the art that allows it to be viewed by researchers as a useful tool in large-scale network problems, sometimes small prototypes can provide solutions of powerful in a simple way and without a high cost of implementation where creativity is the way to find search solutions.

Oppositional geometry gives a mathematical model of oppositional phenomena through “oppositional structures” (logical squares, hexagons, cubes, …). Its so far known formal entities, the backbone of which are the “oppositional bi-simplexes (and poly-simplexes) of dimension m”, are distributed into three families (the alpha-, beta- and gamma-structures). However, some recent studies by different authors exhibit strange structures, notably strange variations of the notion of “oppositional hexagon” (or “logical hexagon”). In this paper we show that inside the oppositional tetrahexahedron, i.e. the beta3-structure (discovered in 1968 and rediscovered in 2008) – a 3D solid made of a logical cube and six logical “strong hexagons”, containing 14 vertices and 36 implication arrows – there are in fact C(6|14) = 30030 strange hexagons, which we call “hybrid hexagons”. In this paper, through a systematic study of those among them which have as invariant property a regular perimeter made of alternated arrows (henceforth “arrow-hexagons”), we show that they divide into a much smaller number of families, nine, each containing several isomorphic instances of the same oppositional pattern. An interesting result seems to be that when seen from the viewpoint of their mutual transformations (i.e. moving from one to another kind of arrow-hexagon, just by exchanging one of its 6 vertices with one among the remaining 14-6=8 vertices of the tetrahexahedron), these arrow-hexagonal patterns taken as points can be displayed into a new kind of 3D structure. The latter, by putting into order these points (each representing a family of arrow-hexagons), gives some kind of morphogenetic cartography of the arrow-hexagons of the beta3-structure. As we will argue, since several arrow-hexagons play the role of “attractors”, there are reasons for thinking that such a cartography could be very meaningful in the future for modelling “oppositional dynamics”, that is the systematic formal study of the situations where a given complex oppositional structure sees its shape change within time.

We develop an intuitive geometric interpretation of the standard support vector machine (SVM) for classification of both linearly separable and inseparable data and provide a rigorous derivation of the concepts behind the geometry. For the separable case finding the maximum margin between the two sets is equivalent to finding the closest points in the smallest convex sets that contain each class (the convex hulls). We now extend this argument to the inseparable case by using a reduced convex hull reduced away from outliers. We prove that solving the reduced convex hull formulation is exactly equivalent to solving the standard inseparable SVM for appropriate choices of parameters. Some additional advantages of the new formulation are that the effect of the choice of parameters becomes geometrically clear and that the formulation may be solved by fast nearest point algorithms. By changing norms these arguments hold for both the standard 2-norm and 1-norm SVM.

We introduce pairwise Stone spaces as a natural bitopological generalization of Stone spaces-the duals of Boolean algebras-and show that they are exactly the bitopological duals of bounded distributive lattices. The category PStone of pairwise Stone spaces is isomorphic to the category Spec of spectral spaces and to the category Pries of Priestley spaces. In fact, the isomorphism of Spec and Pries is most naturally seen through PStone by first establishing that Pries is isomorphic to PStone, and then showing that PStone is isomorphic to Spec. We provide the bitopological and spectral descriptions of many algebraic concepts important for the study of distributive lattices. We also give new bitopological and spectral dualities for Heyting algebras, co-Heyting algebras, and bi-Heyting algebras, thus providing two new alternatives of Esakia's duality.

This tutorial gives an introductive presentation of algebraic and geometric methods for solving a polynomial system f1 = • • • = fm = 0. The first class of methods is based on the study of the quotient algebra A of the polynomial ring modulo the ideal I = (f1,. .. , fm). We show how to deduce the geometry of the solutions, from the structure of A and in particular, how solving polynomial equations reduces to eigen computations of these multiplication operators. We mention briefly two general methods for computing the normal of elements in A, used to obtain a representation of the multiplication operators. The geometric methods are based projection operations, which are closely related to the theory of resultants. We present different notions and constructions of resultants and different methods for solving systems of polynomial equations, based on these formulations. Finally, we illustrate these tools on problems coming from applications in computer vision, robotics, computational biology and signal processing.

This is a rewrite of the paper on here bearing more or less the same title, although it only includes a small number of changes and additions. Although ostensibly on English Literature, the paper really concerns the role of professionals in society, psychiatry and individual identity within human societies.

The following criteria and assumptions are applied: i) all HV nodal voltages to be within the range 0.90-1 .IO p.u. under intact and contingent situations; ii) for simplicity, assume that independence between random variables and no more than one generator or circuit outage happens simultaneously in the studied period.

Semidefinite programming (SDP) is one of the fastest developing branches of mathematical programming. The reason is twofold: efficient solution algorithms for SDP have come to light in the past few years, and SDP finds applications in combinatorial optimization and engineering. In this short survey we show how SDP duality theory can be used to prove classical results, and review the development of interior point algorithms for SDP.

Here the emphasis is on the main pillars of Tarskian structuralist approach to logic: relation algebras, cylindric algebras, polyadic algebras, and Boolean algebras with operators. We also tried to highlight the recent renaissance of these areas and their fusion with new trends related to logic, like the guarded fragment or dynamic logic. Tarskian algebraic logic is far too broad and

Miller McPherson’s approach to measuring the inherent duality of organizational forms and the environmental niches that they occupy is adapted and applied to an analysis of the institutional field of (outdoor) poverty relief organizations operating in New York City (1888-1917).  In contrast to McPherson’s approach which emphasizes how organizations are differentially arrayed within “Blau space,” the focus in this paper concerns how organizational forms are distributed across an institutional “logic space” that is itself dually ordered and defined by the kinds of organizational forms that are understood to exist.  The resulting niche maps are employed to trace out the jurisdictional conflicts that erupted during the Progressive Era between two competing organizational forms — scientific charities and settlement houses —each of which embodied a particular vision and practice for delivering social relief to the poor

The present paper introduces and studies the variety WH of weakly Heyting algebras. It corresponds to the strict implication fragment of the normal modal logic K which is also known as the subintuitionistic local consequence of the class of all Kripke models. The tools developed in the paper can be applied to the study of the subvarieties of WH; among them are the varieties determined by the strict implication fragments of normal modal logics as well as varieties that do not arise in this way as the variety of Basic algebras or the variety of Heyting algebras. Apart from WH itself the paper studies the subvarieties of WH that naturally correspond to subintuitionistic logics, namely the variety of R-weakly Heyting algebras, the variety of T-weakly Heyting algebras and the varieties of Basic algebras and subresiduated lattices. 1) For a definition of the local and the global consequence relations of a normal modal logic see for example [25, Chapter 3].

A new framework is presented for both understanding and developing graph-cut based combinatorial algorithms suitable for the approximate optimization of a very wide class of MRFs that are frequently encountered in computer vision. The proposed framework utilizes tools from the duality theory of linear programming in order to provide an alternative and more general view of state-of-the-art techniques like the α-expansion algorithm, which is included merely as a special case. Moreover, contrary to αexpansion, the derived algorithms generate solutions with guaranteed optimality properties for a much wider class of problems, e.g. even for MRFs with non-metric potentials. In addition, they are capable of providing per-instance suboptimality bounds in all occasions, including discrete Markov Random Fields with an arbitrary potential function. These bounds prove to be very tight in practice (i.e. very close to 1), which means that the resulting solutions are almost optimal. Our algorithms' effectiveness is demonstrated by presenting experimental results on a variety of low level vision tasks, such as stereo matching, image restoration, image completion and optical flow estimation, as well as on synthetic problems.

A relatively simple definition of a locally compact quantum group in the C * -algebra setting will be explained as it was recently obtained by the authors. At the same time we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries and duality theory.

In this paper, the mathematical models of two water distribution network systems, namely a Serial Network and a Branched Network have been considered as nonlinear optimization problems and Particle Swarm Optimization (PSO) method has been used to obtain the global optimal solution in each case. The PSO is a heuristic optimization method. Herein, the PSO has been used to determine the minimum cost of the water distribution network system for a Serial Network and Branched Network. The numerical results indicate the robustness of the PSO method. It suggests that PSO method can be effectively used for any generalized water distribution network system.

The present paper introduces and studies the variety WH of weakly Heyting algebras. It corresponds to the strict implication fragment of the normal modal logic K which is also known as the subintuitionistic local consequence of the class of all Kripke models. The tools developed in the paper can be applied to the study of the subvarieties of WH; among them are the varieties determined by the strict implication fragments of normal modal logics as well as varieties that do not arise in this way as the variety of Basic algebras or the variety of Heyting algebras. Apart from WH itself the paper studies the subvarieties of WH that naturally correspond to subintuitionistic logics, namely the variety of R-weakly Heyting algebras, the variety of T-weakly Heyting algebras and the varieties of Basic algebras and subresiduated lattices. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We introduce a local homology theory for linearly modules which is in some sense dual to the local cohomology theory of A. Grothendieck. Some basic properties of local homology modules are shown such as: the vanishing and non-vanishing, the noetherianness of local homology modules. By using duality, we extend some well-known results in theory of local cohomology of A. Grothendieck.

The usual duality theory cannot be applied to infinite dimensional problems because the underlying constraint set mostly has an empty interior and the constraints are possibly nonlinear. In this paper we present an infinite dimensional nonlinear duality theory obtained by using new separation theorems based on the notion of quasi-relative interior, which, in all the concrete problems considered, is nonempty. We apply this theory to solve the until now unsolved problem of finding, in the infinite dimensional case, the Lagrange multipliers associated to optimization problems or to variational inequalities. As an example, we find the Lagrange multiplier associated to a general elastic-plastic torsion problem.

We consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution. We propose a new portfolio optimization model involving stochastic dominance constraints on the portfolio return. We develop optimality and duality theory for these models. We construct equivalent optimization models with utility functions. Numerical illustration is provided.

We model the Central Bank’s management of intraday liquidity in modern real-time gross settlement systems as an infinite-dimensional linear programming problem parameterized by different intraday monetary policies, such as reserve requirements, net debit caps and Lombard loans. We then use duality theory to determine the shadow-prices of constraints of each bank. These shadow-prices can be used by the Central Bank to set personalized intraday monetary policies in order to reduce idleness of money and to give a microfoundation to the too-big-to-fail policy.

We use a recently developed duality theory for linear differential inclusions (LDIs) to enhance the stability analysis of systems with saturation. Based on the duality theory, the condition of stability for a LDI in terms of one Lyapunov function can be easily derived from that in terms of a Lyapunov function conjugate to the original one in the sense of convex analysis. This paper uses a particular conjugate pair, the convex hull of quadratics and the maximum of quadratics, along with their dual relationship, for the purpose of estimating the domain of attraction for systems with saturation nonlinearities. To this end, the nonlinear system is locally transformed into a LDI system with an effective approach which enables optimization on the local LDI description. The optimization problems are derived for both the convex hull and the max functions, and the domain of attraction is estimated with both the convex hull of ellipsoids and the intersection of ellipsoids. A numerical example demonstrates that the estimation of the domain of attraction by this paper's methods drastically improve those by the earlier methods.

In memory of Willem Blok A b s t r a c t. In this paper, Wójcicki's characterization of selfextensional logics as those logics that are endowed with a complete local referential semantics is extended to a fully fledged duality between atlas-models (i.e. generalized matrix models) and referential models of an arbitrary selfextensional logic S. This duality serves as a general template where a wide range of Stone-and Priestley-style dualities related with concrete logics can fit. The first application of this duality is a characterization of the fully selfextensional logics among the selfextensional ones. Fully selfextensional logics form a subclass of particularly well-behaved selfextensional logics, and only recently [1] this inclusion was shown to be proper. In this paper, fully selfextensional logics are characterized as those selfextensional logics S whose algebraic counterpart Alg(S)-seen as a category-is dually equivalent to the reduced referential models of S. This implies that if S is fully selfextensional, then every algebra in Alg(S) is isomorphic to an algebra of sets.

An inventory model of deteriorating seasonal products with Maximum Retail Price (MRP) for a wholesaler having showrooms at different places under a single management system is considered under random business periods with fuzzy resource constraints. The wholesaler replenishes the products instantaneously and earns commissions on MRP which vary with the ordered quantities following All Unit Discount (AUD), Incremental Quantity Discount (IQD) or IQD in AUD policy. Demand at showrooms are imprecise and related to selling prices by 'verbal words' following fuzzy logic. The wholesaler shares a part of commission with customers. The business periods follows normal distribution and converted to deterministic ones through chance constraint technique. The fuzzy space and budget constraints and fuzzy relations are defuzzified using possibility measures, surprise function and Mumdani fuzzy inference technique. The model is formulated as profit maximization for the wholesaler and solved using a real coded Genetic Algorithm (GA) and illustrated through some numerical examples and some sensitivity analysis. A real-life problem of a developing country is presented, solved using the above mentioned procedures and an appropriate inventory policy is suggested.

The production structure of Tunisian agriculture over the last three decades is investigated using a translog variable cost function. Standard results of neoclassical duality theory are used to obtain measures of elasticities of substitution between inputs, price elasticities of factor demands and the rate of growth and bias of technological progress. Empirical results obtained from the joint estimation of parameters

System performance for networks composed of interconnected subsystems can be increased if the traditionally separated subsystems are jointly optimized. Recently, parallel and distributed optimization methods have emerged as a powerful tool for solving estimation and control problems in large-scale networked systems. In this paper we review and analyze the optimization-theoretic concepts of parallel and distributed methods for solving coupled optimization problems and demonstrate how several estimation and control problems related to complex networked systems can be formulated in these settings. The paper presents a systematic framework for exploiting the potential of the decomposition structures as a way to obtain different parallel algorithms, each with a different tradeoff among convergence speed, message passing amount and distributed computation architecture. Several specific applications from estimation and process control are included to demonstrate the power of the approach.

* Los autores agradecen todas las sugerencias de los evaluadores anónimos, así como las del editor de Desarrollo y Sociedad, porque, sin duda, han permitido mejorar el trabajo de forma considerable. Investigación realizada por el Grupo fecepad con financiación del Gobierno de Aragón y el fondo Social Europeo.

In this paper, we consider the robust stabilization problem for linear discrete time-varying (LTV) systems using the gap metric. In particular, we show that the time-varying (TV) directed gap reduces to an operator with a TV Hankel plus Toeplitz structure. Computation of the norm of such an operator can be carried out using an iterative scheme involving a TV Hankel operator defined on a space of Hilbert-Schmidt causal operators. The "infimization" in the TV directed gap formula is shown to be, in fact, a minimum by using duality theory. The latter holds as well in the time-invariant case.