Multidimensional residues and ideal membership

Some information in this chapter applies only to block storage databases and is not relevant to aggregate storage databases. Also see Comparison of Aggregate and Block Storage. Online analytical processing OLAP is a multidimensional, multiuser, client-server computing environment for users who need to analyze enterprise data. Finance departments use OLAP for applications such as budgeting, activity-based costing allocationsfinancial performance analysis, and financial modeling.

Sales departments use OLAP for sales analysis and forecasting. Typical manufacturing OLAP applications include production planning and defect analysis. Important to all of these applications is the ability to provide managers the information that they need to make effective decisions about an organization's strategic directions.

Providing such information requires more than a base level of detailed data. Just-in-time information is computed data that usually reflects complex relationships and is often calculated on the fly. Analyzing and modeling complex relationships are practical only if response times are consistently short.

In addition, because the nature of data relationships may not be known in advance, the data model must be flexible. A truly flexible data model ensures that OLAP systems can respond to changing business requirements as needed for effective decision making. Although OLAP applications are found in widely divergent functional areas, all require the following key features:. Key to OLAP systems are multidimensional databases, which not only consolidate and calculate data; but also provide retrieval and calculation of a variety of data subsets.

A multidimensional database supports multiple views of data sets for users who need to analyze the relationships between data categories.

For example, a marketing analyst might ask following questions:. How did Product A sell last month? How does this figure compare to sales in the same month over the last five years?

How did the product sell by branch, region, and territory? Did this product sell better in particular regions? Are there regional trends? Did customers return Product A last year?

Were the returns due to product defects? Did the company manufacture the products in a specific plant? Did commissions and pricing affect how salespeople sold the product? Did certain salespeople sell more? In multidimensional databases, the number of data views is limited only by the database outline, the structure that defines all elements of the database.

Users can pivot the data to see information from a different viewpoint, drill down to find more detailed information, or drill up to see an overview. This section introduces the concepts of outlines, dimensions, and members within a multidimensional database. If you understand dimensions and members, you are well on your way to understanding the power of a multidimensional database.

Residues and Duality for Projective Algebraic Varieties

A dimension represents the highest consolidation level in the database outline. The database outline presents dimensions and members in a tree structure to indicate a consolidation relationship. Essbase has standard dimensions and attribute dimensions. Standard dimensions represent the core components of a business plan and often relate to departmental functions.

Dimensions change less frequently than members. Attribute dimensions are associated with standard dimensions. Through attribute dimensions, you group and analyze members of standard dimensions based on the member attributes characteristics. For example, you can compare the profitability of noncaffeinated products that are packaged in glass to the profitability of noncaffeinated products packaged in cans.Ernst Kunz; David A.

Cox; Alicia Dickenstein. This book, which grew out of lectures by E. Kunz for students with a background in algebra and algebraic geometry, develops local and global duality theory in the special case of possibly singular algebraic varieties over algebraically closed base fields.

The properties of residues are introduced via local cohomology.

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Special emphasis is given to the relation between residues to classical results of algebraic geometry and their generalizations. The contribution by A. Dickenstein gives applications of residues and duality to polynomial solutions of constant coefficient partial differential equations and to problems in interpolation and ideal membership.

Cox explains toric residues and relates them to the earlier text. The book is intended as an introduction to more advanced treatments and further applications of the subject, to which numerous bibliographical hints are given. Graduate students and research mathematicians interested in algebra, algebraic geometry, complex analyis, and computer algebra. Know that ebook versions of most of our titles are still available and may be downloaded soon after purchase.

AMS Homepage. Join our email list. Sign up. Advanced search. Cox ; Alicia Dickenstein. Author Misc Blurb: with the assistance of and contributions by David A. Abstract: This book, which grew out of lectures by E. Volume: Publication Month and Year: Copyright Year: Page Count: Cover Type: Softcover. Print ISBN Online ISBN Print ISSN: Online ISSN: Primary MSC: Secondary MSC: Applied Math?

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MAA Book? Inquiry Based Learning? Electronic Media? Apparel or Gift: false. Online Price 1 Label: List. Online Price 1: Print Price 1 Label: List. Print Price 1: Furthermore there are some connections to effective versions of the Nullstellensatz. We also provide explicit integral representations of the solutions.

Integral representation with weights IMath. Ideals of smooth functions and residue currentsJ. Funtional Anal. Residue currents and ideals of holomorphic functionsBull. Analyse Math. Analytic residue theory in the non-complete intersection caseJ. Reine Angew. A formula for division and interpolationMath.

multidimensional residues and ideal membership

Henkin-Ramirez formulas with weightsAnn. FourierTome 32pp. ATomepp. Bounds for the degrees in NullstellensatzAnn. A pure prime product version of the Hilbert NullstellensatzMich. Canonical representatives in moderate cohomologyInvent. A geometric effective NullstellensatzInvent. Effective Nullstellensatz for strictly regular sequencesUniv.

Acta Math. FourierTome 51pp. On the effective Nullstellensatz preprint Zbl Sharp effective NullstellensatzJ. American Math. The algebraic theory of modular systemsCambridge Univ.

multidimensional residues and ideal membership

Press, Cambridge, MR Zbl Residues, currents, and their relation to ideals of holomorphic functionsMath. Residue currents of the Bochner-Martinelli typePubl. Degree bounds for the division problem in polynomial idealsMichigan Math. Multidimensional residues and their applicationsTransl. Residue currents. Complex analysisJ. Informations aux auteurs Soumettre. S'abonner Tarif des abonnements Actes de colloques.

Entre et.Z-number provides the reliability of evaluation information, and it is widely used in many fields. However, people usually describe things from various aspects, so multidimensional Z-number has more advantages over traditional Z-number in describing evaluation information.

In view of the uncertainty of the multidimensional Z-number, the entropy of multidimensional Z-number is defined and an entropy formula of multidimensional Z-number is established.

multidimensional residues and ideal membership

Furthermore, the entropy is used to construct an average operator of multidimensional Z-numbers. In addition, a novel distance measure is introduced to measure the distance between two multidimensional Z-numbers. Moreover, the group decision model in the multidimensional Z-number environment is constructed by combining the average operator with the TOPSIS decision-making method. Finally, an illustrative example is given to verify the feasibility and effectiveness of the proposed method.

In order to solve the problem of uncertain information, Zadeh [ 1 ] added membership function and proposed fuzzy sets FSs theory to solve the problem of quantitative calculation for uncertain information.

However, merely adding membership degree cannot fully express the complexity of the practical problems. Thus, Atanassov [ 2 ] added nonmembership degree and hesitation and introduced intuitionistic fuzzy sets IFSs. Torra [ 3 ] puts forward hesitant fuzzy sets HFSsand it changed membership from single to multiple and gave us the ability to express more possible situation. Mizumoto and Tanaka [ 4 ] proposeed type-2 fuzzy sets by replacing the given elements with intervals for the membership degree.

The extension of fuzzy sets above has been successfully applied to multiattribute decision-making MADM problems [ 5 — 12 ]. However, the classical fuzzy set and its extension do not give the reliability measurement of evaluation information.

It combined the objective information of natural language with the subjective understanding of human beings by constraint and reliability. After the concept of Z-number was proposed, many scholars have conducted in-depth research on Z-number, it can be roughly divided into two categories. The first category is theoretical research and expansion.

In [ 1415 ], Aliev et al. Kang et al. It contributed to the theory and methods on the classical fuzzy set which were applied to the Z-number environment. Yager and Ronald [ 17 ] discussed several special hidden probability distributions of - number. It reinforced the capability of Z-numbers by virtue of parameters incorporating the context and time and affects embedded in natural language sentences.

Sometimes the information was useful if some conditions were true; Allahviranloo and Ezadi [ 20 ] investigated Z-advance numbers, aiming to solve the uncertain information problem which was reliable depends on some conditions. The second category is the practical application of Z-numbers; many scholars applied Z-number to linguistic calculation [ 2122 ], and some used it as a tool for fuzzy inference [ 23 ] and pattern recognition [ 24 ].

Z-number is more likely to be used for MADM. Wang et al.PL EN. Widoczny [Schowaj] Abstrakt. Adres strony. Banach Center Publications.

Residue currents and complexity problems. ElkadiA. Institute of Mathematics Polish Academy of Sciences. Opis fizyczny. Aizenberg and A. Amoroso, Bounds for the degrees in the membership test for a polynomial ideal, Acta Arith. Kollar, C. I Philippon ed.

Amoroso, On a conjecture of C. Berenstein and A. Yger, in: Proc. MEGA 94, Progr. Amoroso, The membership problem for smooth ideals, Publ. Curie, to appear. Amoroso, The membership problem for 'almost' complete intersection ideals, preprint. Atiyah, Resolution of singularities and division of distributions, Comm. Pure Appl. Bayer and M. Stillman, On the complexity of computing syzygies, J.Sirius Mathematics Center is an international institution for research and postgraduate training in mathematical sciences established in by the "Talent and Succes" Educational Foundation.

The Center strives to be a meeting point for scientists working in mathematical sciences to exchange ideas, initiate new projects, meet and train students and young scientists. The Scientific Board is responsible for establishing selection criteria for proposals of activities at the SMC, evaluation of the proposals and developing the Scientific Program of the Center.

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The current members are. The regular activities of the Center include week-long workshops, schools for young researchers, and group work meetings. Read more. The Center accepts applications for workshops, schools for young researchers, and group work meetings to be held in The deadline for applications is September 6, Please follow these guidelines in your application.

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Description: Integral representations and residues is a powerful tool for studying functions and computing integrals. By integrals one can represent a number of solutions of a system of equations, the roots, solutions to differential equations, many special functions of mathematical physics. As a rule, construction of residues is closely related to analytic sets; therefore, the residue theory goes deep into algebraic geometry, in particular in the problem of ideal membership and the effective Nulstellensatz.

In the last decades the ideas of the multidimensional residue theory proved to be useful in tropical geometry thanks to important notions of the Jensen-Ronkin counting function and of a supercurrent, which is related to the Monge-Ampere problem in the pluripotential theory. In the last decades the studies led to discovery of new regularizations of residue currents, Koppelman formulas for solution of a d-bar problem on analytic sets. There have been constructed residue currents associated to weakly holomorphic functions; a non-standard interpolation problem for holomorphic functions has been solved using the Grothendieck residues; a k-convexity according to Gromov for a complement of an amoeba for a complete intersection has been proved.

The major topic for discussions during the proposed workshop are: k-convexity according to Gromov for complements of amoebas in case of incomplete intersections; tropical Hodge theory; tropical version of the Gelfond-Khovansky theorem; logarithmic Gauss mapping and non-standard interpolation in analytic spaces; computation of the Mellin-Barnes integrals with applications to mathematical physics.

Description: The goal of the workshop is to bring together leading experts to discuss the latest achievements in the area of complex approximations and orthogonal polynomials. The main direction of the workshop is to communicate recent results in the theory of rational approximation of analytic functions.

Important tools for rational approximation are the Riemann-Hilbert problems, the theory of orthogonal polynomials, the theory of the logarithmic potential and the operator theory for difference operators.The accidental discovery of the antibiotic penicillin, by Alexander Fleming in the late s, reshaped human and animal medicine.

Initially the focus was on limiting the impact of infectious disease processes in humans. As their usage increased, it was observed that they also could play an important role in the production of animals and they eventually were deemed essential to provide a burgeoning human population with high quality, safe and cheap animal protein.

The feeding of antibiotics from birth to slaughter became a standard operating practice for many different animals. This transition from a fishery to a farmed product has brought with it many of the challenges that face terrestrial agriculture as well as some that are uniquely aquatic. A great deal of research has shed substantial light on what Dr. Many antibiotics are in use today, with the most powerful being synthetic and frequently derived from natural sources.

Commercialization is a very expensive proposition, requiring working with multiple government agencies and a large amount of testing. Once a broad-ranging arsenal of antimicrobial substances was established, the incentives to develop others waned. Today, only a small fraction of what has been spent historically to develop antibiotics has been allocated towards the development of new antimicrobial substances.

As their use and availability have increased, it became evident that the pathogens that we were trying to keep from killing humans and animals were developing resistance, limiting the usefulness of these very important tools. Conservative estimates are that more than 1 million people a year die from infections with antibiotic-resistant pathogens.

By the yearthis is estimated to significantly grow to more than 10 million people dying annually. These are deaths that would be preventable if the widespread use of antibiotics not just abuse was curtailed. Most countries regulate, to some extent, what and how antibiotics can be used. Enforcement, though, may be lax or nonexistent, allowing indiscriminate use to flourish.

The reasons for this are complex. Focusing on shrimp farming, perhaps the single-largest reason for the widespread use of antibiotics is that the traditional and widely used farming practices are not science-based. All too often when farmers have animal health challenges, they have no idea what is actually going on. While a competent authority may isolate and identify potential pathogens, disease is often multifactorial with multiple pathogens and stressors playing a role.

Few farmers, if they look at all, look further than a single possible culprit. Researchers examine antimicrobial resistance potential in aquaculture. Most farmed shrimp is produced by small farmers in what is largely a poverty-driven production system.

They may operate one or two small ponds on their property and have a considerable portion of their wealth tied up in the ponds. Poor outcomes, all too common, are disastrous and many resort to the use of readily available antibiotics, whether legal or not, in an effort to avoid serious financial repercussions. The farmer, often in desperation, uses every tool at his disposal to try and salvage his profits when animals are dying. When antibiotics are used properly, i. Unfortunately, this information is simply not available to most shrimp farmers and they gamble that they will see a benefit and that there will be no easy way that their use of an antibiotic can be determined.

It is ironic that physicians also play a role in the overuse of antibiotics by prescribing them in the absence of proof that they are indicated. There are many that think that this is actually the predominant reason for the development of resistance.

In Southeast Asia where most of the worlds farmed shrimp is produceda common practice is to pool the harvests from a number of small farmers into a single lot. This ensures that traceability is not always complete and indeed it is often lost. So, a farmer may use a specific antibiotic that his local feed mill, processing plant, animal health consultant or other source recommends — far too often with no regard for the proper usage — and gamble that its presence will not be discovered.

Poverty-driven production paradigms are highly susceptible to this abuse. Farmers who would go bankrupt from single crop failures make choices that are understandable, even if irresponsible and in the long run, foolish.


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