Digital Commons Network^™

Centric Cardinal Sine Function, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

According to any standard dictionary, the word "cardinal" is synonymous with "principal", "essential", "fundamental". In centric mathematics (CM), or ordinary mathematics, cardinal is, on the one hand, a number equal to a number of finite aggregate, called the power of the aggregate, and on the other hand, known as the sine cardinal sinc(x) or cosine cardinal cosc(x), is a special function defined by the centric circular function (CCF). sin(x) and cos(x) are commonly used in undulatory physics (see Figure 1) and whose graph, the graph of cardinal sine, which is called as "Mexican hat" (sombrero) because of its shape.

Neutrosophic Masses & Indeterminate Models Applications To Information Fusion, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we introduce the indeterminate models in information fusion, which are due either to the existence of some indeterminate elements in the fusion space or to some indeterminate masses. The best approach for dealing with such models is the neutrosophic logic.

Mammalogy Class 2012 Catalog, Vanessa Casias

Division of Mammals - Field Notes and Catalogs

No abstract provided.

Mammalogy Class 2012 Field Notes, Vanessa Casias

Division of Mammals - Field Notes and Catalogs

No abstract provided.

Bulletin And Handbook Of Policies, 2011-2012, University Of New Mexico School Of Law

Bulletin and Handbook of Policies

This Bulletin and Handbook of Policies, 2011-2012 reflects the current policies of the University of New Mexico School of Law and is intended as a source of information for questions concerning the Rules and Regulations of the Law School and other matters pertaining to a students law school career.'

Lines Of Tribe, Christine Zuni Cruz

Faculty Scholarship

It is important to begin by explaining why I take the title of my essay from the statement in President Barack Obama's 2009 Inaugural Address: "the lines of tribe shall soon dissolve." During the address, his words affected me and they remained with me long afterward. President Obama may very well have meant what he said in a metaphoric or figurative sense; I have certainly been provided with many interpretations and assurances by most that a literal meaning was not his intent and that he instead spoke in a good way of the beneficial melting of divisions between us." It …

A Modest Proposal: The Aged Of Death Row Should Be Deemed Too Old To Execute, Elizabeth Rapaport

Faculty Scholarship

My exploration of the case for an Eighth Amendment bar against executing the long-serving elderly will begin with a review of the representation of the elderly on Americas death rows and a survey of the very limited avenues of relief currently available to them on the basis of age. I will then discuss the attribution problem by asking at whose door should 'fault' for long delays between condemnation and consummation of a capital sentence be laid--the prisoner, the state, or the working through of due process? For many jurists, attribution of fault is critical to resolving the question of whether …

Science Council Committee, Andrews Forest, May, 2012, Long Term Ecological Research Network

Long Term Ecological Research Network

No abstract provided.

Did You Say Library Anxiety? (Part 1 & 2), Marquita Harnett

Faculty Scholarship

"Most people are familiar with the terms test anxiety, math anxiety, performance anxiety, computer anxiety, or even social anxiety. But mention "library anxiety" and you'll likely get a response similar to, "Library what?" Library anxiety is not a well-known phenomenon, even among librarians. The bulk of research on library anxiety has concentrated on the problem as it applies to university students, but it's not hard to imagine that it manifests itself in library patrons across the board. Where did this idea come from, how can librarians identify it, what steps can be taken to reduce it and what can the …

Beyond Best Practices For Legal Education: Reflections On Cultural Awareness - Exploring The Issues In Creating A Law School And Classroom Culture, Antoinette M. Sedillo Lopez

Faculty Scholarship

If law schools are to prepare students for the reality of practice, it is useful to help students become aware of cultural issues that can affect client representation by examining the culture that the law school creates. The culture created by faculty, students, administration, and staff will affect the law student's acculturation as a legal professional as well as the law student's psychological well-being. This issue was addressed briefly in Best Practices for Legal Education (Best Practices), but not developed. This essay explores some of the challenges and opportunities of bringing cross-cultural issues into a law school classroom and some …

Brief For Thirteenth Amendment Scholars, United States V. Hatch As Amicus Curiae, Dawinder S. Sidhu

Faculty Scholarship

Like the district court, we conclude that Congress has power under the Thirteenth Amendment to enact § 249(a)(1). Although the Thirteenth Amendment by its terms applies to slavery and involuntary servitude, Supreme Court precedent confirms Congress’s authority to legislate against slavery’s “badges and incidents” as well. In particular, the Supreme Court held in Jones v. Alfred H. Mayer Co., 392 U.S. 409 (1968)—a case permitting a federal private right of action against private individuals for housing discrimination—that Congress itself has power to determine those badges and incidents.

Federal Water Law And The 'Double Whammy': How The Bureau Of Reclamation Can Help The West Adapt To Drought And Climate Change, Reed D. Benson

Faculty Scholarship

No abstract provided.

Public Funding Programs For Environmental Water Acquisitions: Origins, Purposes, And Revenue Sources, Reed D. Benson

Faculty Scholarship

No abstract provided.

Alive But Irrelevant: The Prior Appropriation Doctrine In Today’S Western Water Law, Reed D. Benson

Faculty Scholarship

The Prior Appropriation Doctrine has long been the foundation of laws governing water allocation and use in the American West, but it has been under pressure from forces both external and internal to the western states. Twenty years ago, Prior Appropriation was pronounced dead in a provocative essay by Charles Wilkinson. Other scholars argued that it was still alive, but it now appears to have lost its force as the controlling doctrine of western water law. This Article analyzes three recent cases upholding state laws that undermine a fundamental Prior Appropriation principle, then considers the water policy implications of the …

R2p= Mdgs: Implementing The Responsibility To Protect Through The Millennium Development Goals, Jennifer Moore

Faculty Scholarship

This essay is a peaceful call to arms based on the understanding that an essential way to fight the most egregious and widespread human rights abuses is through a broad-spectrum approach to human security grounded in the Millennium Development Goals and a new, non-military, understanding of humanitarian intervention. The responsibility to protect, often cited as a justification for military force to stop genocide, crimes against humanity, and other widespread human rights abuses, is better seen as a commitment by all nations to strengthen their own social welfare and human rights systems, and for those nations with more resources to assist …

The Bowl Championship Series, Conference Realignment And The Major College Football Oligopoly: Revolution Not Reform, Alfred Dennis Mathewson

Faculty Scholarship

The legality of the Bowl Championship Series under the federal antitrust laws has been the subject of much scholarly commentary and Congressional inquiry. The results have been mixed but the majority view seems to be that the BCS passes muster under the Sherman Act. Most of the commentary has examined the application of Section 1 with only passing attention to Section 2. This article makes three points. First, it argues that the focus on the BCS has obscured the attention to a broader set of economic issues relating to the structure of the major college football industry. The Bowl Championship …

Remediating Discrimination Against African American Females At The Intersection Of Title Ix And Title Vi, Alfred Dennis Mathewson

Faculty Scholarship

In Part I, I present a brief treatment of intersectionality in anti-discrimination law focusing on the distinction between cause of action and remedy. Harm caused by gender or racial discrimination may give rise to causes of action based on equal protection principles." In Part II, I go further and argue that the primary intersectionality problem presented by Title IX is one of remedy. I conclude that the differences in the remedial effects of Title IX result, in part, from unremedied racial discrimination, a conclusion that begins with Professor Jerome Dees's argument that Brown v. Board of Education and anti-discrimination laws …

Environmental Law, Civil Rights And Sustainability: Three Frameworks For Environmental Justice, Eileen Gauna

Faculty Scholarship

This article focuses on the domestic context, where the issues have more concretely crystallized around viewing environmental justice issues from a civil rights framework, and also from a competing environmental law framework. The article will begin with a discussion of the limitations of each of these frameworks, and will then explore the current "disconnect" between these two models, ending with an exploration of how the principles of sustainability fit into the picture. As to the latter point, sustainability is a double-edged sword. It might be used to maintain the inequity of the status quo; and, particularly in light of climate …

Why Agencies Punish, Max J. Minzner

Faculty Scholarship

In addition to promulgating regulations, federal administrative agencies penalize entities that violate their rules. In 2010 alone, the National Highway Traffic Safety Administration imposed a statutory maximum $16.4 million penalty on Toyota, and the Securities and Exchange Commission recovered $535 million from Goldman Sachs, the largest civil penalty a financial services firm has ever paid. The academic literature proposes two major theories explaining why agencies might seek these monetary penalties. First, agencies might seek to deter misconduct by using civil penalties to raise the expected cost of regulatory violations above the cost of compliance. Alternatively, agencies might use civil penalties …

Performance Isn't Everything: The Importance Of Conceptual Competence In Outcome Assessment Of Experiential Learning, Serge A. Martinez, Stefan H. Krieger

Faculty Scholarship

This article scrutinizes—and ultimately rejects—the recommendations of the Carnegie Report for outcome assessments in experiential legal education. The Carnegie Report argues that practical education should focus on teaching students to mimic the actions of expert lawyers by encouraging students to follow expert protocols, procedures, rules, and checklists that can enable them to deal effectively with lawyering situations. To the contrary, however, an extensive body of cognitive science and neuroscienceresearch on the development of expertise questions the theoretical underpinnings of the Carnegie Report and suggests that educators should focus not on what experts are doing but on what they are thinking …

The Alliance Between Payday Lenders And Tribes: Are Both Tribal Sovereignty And Consumer Protection At Risk?, Nathalie Martin

Faculty Scholarship

This Article explores how tribal sovereign immunity is being used in the context of payday lending to avoid state law and explores the ramifications of this for both consumer-protection regulation and tribes. It discusses payday loans and tribal sovereignty generally, as well as tribal sovereign immunity, then discusses what might be done to address this consumer protection issue. More specifically, we discuss who in society has the power and resolve to dissolve this alliance, identifying tribes themselves, the Supreme Court, Congress, the Federal Trade Commission, and the Consumer Financial Protection Bureau as possibilities. We summarize the debate about whether payday …

Superluminal Physics And Instantaneous Physics As New Trends In Research, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In a similar way as passing from Euclidean Geometry to Non-Euclidean Geometry, we can pass from Subluminal Physics to Superluminal Physics, and further to Instantaneous Physics. In the lights of two consecutive successful CERN experiments with superluminal particles in the Fall of 2011, we believe that these two new fields of research should begin developing.

Extenics In Higher Dimensions, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Prof. Dr. Florentin Smarandache, during his research period in the Summer of 2012 at

the Research Institute of Extenics and Innovation Methods, from Guangdong University of

Technology, in Guangzhou, China, has introduced the Linear and Non-Linear Attraction

Point Principle and the Network of Attraction Curves, he has generalized the 1D Extension

Distance and the 1D Dependent Function to 2D, 3D, and in general to n-D Spaces, and he

generalized Qiao-Xing Li’s and Xing-Sen Li’s definitions of the Location Value of a Point

and the Dependent Function of a Point on a Single Finite Interval from one dimension (1D) …

Quantization And Discretization At Large Scales, Florentin Smarandache, Victor Christianto, Pavel Pintr

Branch Mathematics and Statistics Faculty and Staff Publications

The ongoing search of extrasolar planets is one of the most attractive fields of research in astrophysics and astronomy. Up to now, 360 extrasolar planets have been discovered near stars with similar mass as the Sun. There is also discovery related to the so-called Earth-like planets. With regards to these discoveries, one intriguing question is whether there is relationship between orbit distance of the planets and their stars. Various formulas have been suggested since 1990s, and they suggest that there may be reason to accept quantization of distances of those planets both in our solar system and also in extrasolar …

Vacuum, Space-Time, Matter And The Models Of Smarandache Geometry, Florentin Smarandache, Hu Chang-Wei

Branch Mathematics and Statistics Faculty and Staff Publications

Many fundamental concepts in physics remain unsolved:  What is time? Is it pure relative?  What is the vacuum? Is it void space or special medium?  What is mass? Can it be created? I believe that physicists have not got definite answers for the above questions. Isaac Newton said: I was like a boy playing on the sea-shore, and diverting myself now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me. For instance, we still do not know what the clear definition of time …

Innovative Uses Of Matrices, Florentin Smarandache, W.B. Vasantha Kandasamy, Indra Venkatbabu

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors bring out the innovative applications of matrices defined, described and developed by them. Here they do not include the natural product on matrices newly described and defined by them in the book on ‘natural product ×n on matrices’.

This book is organized into seven chapters. The first one is introductory in nature. In the second chapter authors give the unique and new way of analyzing the data which is time dependent. We construct three types of matrices called Average Time Dependent data matrix (ATD matrix), Refined Time Dependent Data matrix (RTD matrix) and Combined Effective Time …

Supermodular Lattices, Florentin Smarandache, Iqbal Unnisa, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In lattice theory the two well known equational class of lattices are the distributive lattices and the modular lattices. All distributive lattices are modular however a modular lattice in general is not distributive.

In this book, new classes of lattices called supermodular lattices and semi-supermodular lattices are introduced and characterized as follows: A subdirectly irreducible supermodular lattice is isomorphic to the two element chain lattice C2 or the five element modular lattice M3. A lattice L is supermodular if and only if L is a subdirect union of a two element chain C2 and the five element modular lattice M3.

Special Quasi Dual Numbers And Groupoids, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the authors introduce a new notion called special quasi dual number, x = a + bg.

Among the reals – 1 behaves in this way, for (– 1)2 = 1 = – (– 1). Likewise –I behaves in such a way (– I)2 = – (– I). These special quasi dual numbers can be generated from matrices with entries from 1 or I using only the natural product ×n. Another rich source of these special quasi dual numbers or quasi special dual numbers is Zn, n a composite number. For instance 8 in Z12 is such that …

Special Dual Like Numbers And Lattices, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the authors introduce a new type of dual numbers called special dual like numbers. These numbers are constructed using idempotents in the place of nilpotents of order two as new element. That is x = a + bg is a special dual like number where a and b are reals and g is a new element such that g2 =g. The collection of special dual like numbers forms a ring. Further lattices are the rich structures which contributes to special dual like numbers. These special dual like numbers x = a + bg; when a and b …

Non Associative Linear Algebras, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the notion of non associative vector spaces and non associative linear algebras over a field. We construct non associative space using loops and groupoids over fields. In general in all situations, which we come across to find solutions may not be associative; in such cases we can without any difficulty adopt these non associative vector spaces/linear algebras. Thus this research is a significant one.

This book has six chapters. First chapter is introductory in nature. The new concept of non associative semilinear algebras is introduced in chapter two. This structure is …