Physical Sciences and Mathematics Commons^™

Principal Angles And Approximation For Quaternionic Projections [Dataset], Terry A. Loring

Math and Statistics Datasets

We extend Jordan's notion of principal angles to work for two subspaces of quaternionic space, and so have a method to analyze two orthogonal projections in the matrices over the real, complex or quaternionic field (or skew field). From this we derive an algorithm to turn almost commuting projections into commuting projections that minimizes the sum of the displacements of the two projections. We quickly prove what we need using the universal real C*-algebra generated by two projections.

Estimating Norms Of Commutators [Dataset], Terry A. Loring, Freddy Vides

Math and Statistics Datasets

We find estimates on the norm of a commutator of the form [f(x),y] in terms of the norm of [x,y], assuming that x and y are bounded linear operators on Hilbert space, with x normal and with spectrum within the domain of f. In particular we discuss |[x^2,y]| and |[x^{1/2},y]| for 0leq x leq 1. For larger values of delta = |[x,y]| we can rigorous calculate the best possible upper bound |[f(x),y]| leq eta_f(delta) for many f. In other cases we have conducted numerical experiments that strongly suggest that we have in many cases found the correct formula for the …

Estimating Norms Of Commutators, Terry A. Loring, Freddy Vides

Branch Mathematics and Statistics Faculty and Staff Publications

We find estimates on the norm of a commutator of the form $[f(x),y]$ in terms of the norm of $[x,y]$, assuming that $x$ and $y$ are bounded linear operators on Hilbert space, with $x$ normal and with spectrum within the domain of $f$. In particular we discuss $\|[x^2,y]\|$ and $\|[x^{1/2},y]\|$ for $0\leq x \leq 1$. For larger values of $\delta = \|[x,y]\|$ we can rigorous calculate the best possible upper bound $\|[f(x),y]\| \leq \eta_f(\delta)$ for many $f$. In other cases we have conducted numerical experiments that strongly suggest that we have in many cases found the correct formula for the …

Computing A Logarithm Of A Unitary Matrix With General Spectrum [Dataset], Terry A. Loring

Math and Statistics Datasets

We analyze an algorithm for computing a skew-Hermitian logarithm of a unitary matrix, and also skew-Hermitian approximate logarithms for nearly unitary matrices. This algorithm is very easy to implement using standard software and it works well even for unitary matrices with no spectral conditions assumed. Certain examples, with many eigenvalues near -1, lead to very non-Hermitian output for other basic methods of calculating matrix logarithms. Altering the output of these algorithms to force an Hermitian output creates accuracy issues which are avoided by the considered algorithm. A modification is introduced to deal properly with the J-skew symmetric unitary matrices. Applications …

The Biophysical Effects Of Deuterium Oxide On Biomolecules And Living Cells Through Open Notebook Science., Anthony Salvagno

Physics & Astronomy ETDs

This dissertation explores various effects of deuterium oxide (D2O also known as heavy water) in nature. Water is everywhere and interacts with just about everything. As such, it would be quite a daunting task to characterize every effect that water exhibits on everything in the universe. This research is a small piece of the puzzle, and provides some fundamental understanding of how water interacts with other molecules. This is done from two viewpoints: (1) the effects of heavy water on living cells and (2) the effects of heavy water on molecules. Varying concentrations of deuterium oxide were used as the …

Examples Where The Conjunctive And Dempster’S Rules Are Insensitive, Florentin Smarandache, Jean Dezert, Valeri Kroumov

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we present several counter-examples to the Conjunctive rule and to Dempster rule of combinations in information fusion.

A Journey Into Quantization In Astrophysics, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

The present book consists of 17 select scientific papers from ten years of work around 2003-2013. The topic covered here is quantization in Astrophysics. We also discuss other topics for instance Pioneer spacecraft anomaly. We discuss a number of sub-topics, for instance the use of Schrödinger equation to describe celestial quantization. Our basic proposition here is that the quantization of planetary systems corresponds to quantization of circulation as observed in superfluidity. And then we extend it further to the use of (complex) Ginzburg-Landau equation to describe possible nonlinearity of planetary quantization. Some of these papers have been published in journal …

On Fuzzy Soft Matrix Based On Reference Function, Florentin Smarandache, Said Broumi, Mamoni Dhar

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we study fuzzy soft matrix based on reference function. Firstly, we define some new operations such as fuzzy soft complement matrix and trace of fuzzy soft matrix based on reference function. Then, we introduced some related properties, and some examples are given. Lastly, we define a new fuzzy soft matrix decision method based on reference function.

Relations Between Distorted And Original Angles In Str, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Using the Oblique-Length Contraction Factor, which is a generalization of Lorentz Contraction Factor, one shows several trigonometric relations between distorted and original angles of a moving object lengths in the Special Theory of Relativity.

A Rigid, Thermally-Isolating Suspension For An Adr, Ruslan Hummatov, Linh N. Le, Felix T. Jaeckel, S. T. P. Boyd

Physics & Astronomy Faculty and Staff Publications

We have recently developed a scanning optical pulser for the precise measurement of device-to-device reproducibility, position-dependent response, and other important characteristics of low-temperature particle detectors. By making maps of the reflected light, we can measure the position of the detectors (mounted on the ADR) under the scanner (mounted on the 3K flange) to micro-meter precision . We find that the detector position typically changes approximately 3-4 μm from ADR regeneration to ADR regeneration . Further, when the ADR is allowed to warm at zero field over many hours from its base temperature to approximately 1 K, an additional change in …

Neotectonic Evolution Of Grand Canyon : Interaction Between Volcanism, River Incision, Epeirogenic Uplift, And Faulting, Ryan Crow

Earth and Planetary Sciences ETDs

This thesis focuses on the effects of volcanism, river incision, epeirogenic uplift, and faulting on the landscape evolution of the Grand Canyon region. In the first chapter the migration of increasingly asthenospheric basaltic volcanism is used to constrain lithospheric modification of the Colorado Plateau margins. Buoyancy modification of the upper mantle, driven by the upwelling, is a likely driver for recent uplift of the area. In the second chapter, correlation between oversteepened rivers and areas of high-velocity upper mantle is used to show that recent and ongoing mantle-driven uplift is modulating the surface along the western margin of the Colorado …

American Indian Water Rights, Michael Osborn, Darcy S. Bushnell

Water Matters!

Pueblos and tribal reservations are located within most of the larger stream systems in New Mexico. Each has claims to rights to use the water in its stream. In New Mexico, Indian rights are significant because of their early priority dates, because of the large amounts of water rights claimed, or both. In some instances, such claims have the potential to displace a significant number of junior water rights.

Common law theories or doctrines pertaining to Indians continue to be judicially refined and to evolve so that discussing the nature and extent of “Indian water rights” is a complex topic.

State And Regional Water Planning, Brigette Buynak, Susan Kelly, Sarah Armstrong

Water Matters!

A statewide water planning effort was initiated by the New Mexico legislature in the 2003 session. The Interstate Stream Commission (ISC),in collaboration with the Office of the State Engineer (OSE) and the Water Trust Board, was tasked with preparing and implementing a comprehensive state water plan. Regional water planning had begun much earlier, prompted by a lawsuit that El Paso filed against New Mexico in 1983, El Paso v. Reynolds.

The State Water Plan Act of 2003 (Act) was intended to promote stewardship of the state’s water resources and to establish clear policies and strategies for management of the state’s …

Groundwater, Darcy S. Bushnell, Diego Urbina

Water Matters!

Since the late nineteenth century, New Mexicans have been developing the state’s groundwater resources. From hand-dug wells to proposed wells that could penetrate to 12,000 feet, residents have sought sources to supplement and replace surface water. The state relies upon groundwater to supply almost 50 percent of its needs.

As the population grows and drought intensifies, groundwater sources are tapped with increasing urgency. Limited steps are being taken to preserve groundwater through conservation, groundwater recharge, and regulation.

Deep Water Regulation, Paul Bossert, Kari Olson

Water Matters!

With most of the surface water in New Mexico fully appropriated and with groundwater sources being drawn down and becoming less reliable, the search for new sources of water is reaching further and further afield of traditional sources and methods. Water wells deeper than 2,000 feet have been rare due to the expense of deep drilling and the uncertainty of finding potable water. Yet the combined circumstances of advances in hydrology and the escalating demand for new water have driven the search for water deeper than was previously considered practical.

Community Water Systems, Joanne Hilton, Susan Kelly, Sarah Armstrong

Water Matters!

Apart from the major cities along the Rio Grande corridor, much of New Mexico remains relatively rural. Recent studies estimate a 2013population of around 2,085,500 statewide. In the state fiscal year 2011,about 1,836,000 people, or 88 percent of New Mexico’s population obtain their water from community water systems. Approximately 284,000 people, or about14 percent of the population, receive their drinking water from community water systems serving fewer than 5,000 people. As of 2012, there are 1,148 public water systems that provide drinking water in New Mexico. Of these systems, 593are community water systems; of these, 546 serve fewer than 5,000 …

Water Marketing, Jeremy Oat, Laura Paskus

Water Matters!

Water doesn’t just flow around New Mexico in streams and rivers: it also moves around on paper. Since all of the state’s surface-water and most of its groundwater have already been allocated, the only way for cities, developers, or conservation organizations to find new water supplies is to buy and transfer water rights from old uses and places to new uses and places. The N.M. Office of the State Engineer (OSE) approves each of these transfers, most of which are relatively small, but the numbers can add up over time. Between 1982 and 2011, for instance, 21,000 acre-feet of Middle …

Water Litigation In The Lower Rio Grande, Darcy S. Bushnell

Water Matters!

The water allocation issues are hotly contested in south-central New Mexico and the surrounding area. Today, the river and those who depend on it face more administrative challenges in the face of shrinking water supplies and increased population. These challenges have given rise to two ongoing lawsuits: the Lower Rio Grande Adjudication,New Mexico v. EBID, et al., 96-CV-888 (1996) (N.M. v. EBID) in the New Mexico Third Judicial District Court (adjudication court) and the New Mexico v. United States,et al., D.N.M. 11-CV-691 (2011) (N.M. v.U.S.) in United States District Court of New Mexico (U.S. District Court).

The Rio Grande As An International River, Margaret J. Vick

Water Matters!

The Rio Grande is divided into two major river reaches and has different legal regimes for each. New Mexico is primarily concerned with the Rio Grande from the headwaters in Colorado to Ft. Quitman in Texas, a distance of approximately 670 miles. This section of the river is the subject of the1906 Rio Grande Convention (Treaty) between the United States and Mexico. The lower section of the Rio Grande from Ft. Quitman to the Gulf of Mexico is the subject of the 1944 Rivers Treaty between the United States and Mexico; the 1944 Rivers Treaty also includes the Colorado and …

Eastern New Mexico Rural Water System (Ute Pipeline Project), Jerold Widdison, Paul Van Gulick, Darcy S. Bushnell

Water Matters!

The Ute Pipeline Project (Project), officially known as the Eastern New Mexico Rural Water System (ENMRWS),is a 151-mile-long pipeline project to provide a sustainable municipal and industrial water supply for several eastern New Mexico communities and a military base. The Congress authorized major federal funding for the Ute Pipeline in the Omnibus Public Land Management Act of 2009. This important milestone for the project was reached after about 45 years of effort.Attention now shifts to myriad details involved in actually constructing, financing,and administering the project.

The Hyperbolic Menelaus Theorem In The Poincare Disc Model Of Hyperbolic Geometry, Florentin Smarandache, Catalin Barbu

Branch Mathematics and Statistics Faculty and Staff Publications

In this note, we present the hyperbolic Menelaus theorem in the Poincar´e disc of hyperbolic geometry.

Fuzzy Neutrosophic Models For Social Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, authors give the notion of different neutrosophic models like, neutrosophic cognitive maps (NCMs), neutrosophic relational maps (NEMs), neutrosophic relational equations (NREs), neutrosophic bidirectional associative memories (NBAMs) and neutrosophic associative memories (NAMs) for socio scientists. This book has six chapters. The first chapter introduces the basic concepts of neutrosophic numbers and notions about neutrosophic graphs which are essential to construct these neutrosophic models. In chapter two we describe the concept of neutrosophic matrices and the essential operations related with them which are used in the study and working of these neutrosophic models. However the reader must be familiar …

Correlation Coefficient Of Interval Neutrosophic Set, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we introduce for the first time the concept of correlation coefficients of interval valued neutrosophic set (INS for short). Respective numerical examples are presented.

Indeterminate Masses, Elements And Models In Information Fusion, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper at the beginning, we make a short history of the logics, from the classical Boolean logic to the most general logic of today neutrosophic logic. We define the general logic space and give the definition of the neutrosophic logic. Then 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, which is part of neutrosophy. Neutrosophic logic is connected with neutrosophic set and neutrosophic probability and statistics.

Acequias, Brigette Buynak, Jerold Widdison, Darcy S. Bushnell

Water Matters!

Acequias are community irrigation systems in the villages and pueblos of New Mexico. They have deep roots in two ancient traditions—Pueblo Indian and Spanish. The Pueblos collected and shared water for centuries before the arrival of Spanish colonists in 1598. The Spanish settlers brought technical knowledge and institutional frameworks for governing irrigation systems, which originated in the Moors’ seven-century occupation of Spain. Both traditions remain important to an understanding of New Mexico’s acequia heritage and the continuing relevance of these “water democracies.”Today, these traditions must meld with state law as the legislature has provided that acequias are “political subdivisions” or …

Water Quality Regulation, Joanne Hilton, Susan Kelly, James Hogan, Kimberly Kirby, Jerry Schoeppner

Water Matters!

While many of the water issues in New Mexico center around having an adequate supply of water, the quality of the water is just as important as the quantity in supplying water for drinking and other uses that rely on clean water. Protecting water quality is financially more feasible than conducting expensive cleanup programs. New Mexico has a strong interest in water quality regulation to protect public health and the environment and to minimize expenditures for mitigation of contaminated supplies. Water quality is a difficult subject to navigate; there is a complex web of statutes and agency involvement. This paper …

Unsolved Problems In Special And General Relativity, Florentin Smarandache, Fu Yuhua, Zhao Fengjuan

Branch Mathematics and Statistics Faculty and Staff Publications

This book includes 21 papers written by 23 authors and co-authors. All papers included herein are produced by scholars from People’s Republic of China, except two papers written by Prof. L. Sapogin, V. A. Dzhanibekov, Yu. A. Ryabov from Russia, and by Prof. Florentin Smarandache from USA. The editors hope that all these papers will contribute to the advance of scholarly research on several aspects of Special and General Relativity. This book is suitable for students and scholars interested in studies on physics. The first paper is written by Hua Di. He writes that Einstein’s general theory of relativity cannot …

Subset Polynomial Semirings And Subset Matrix Semirings, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors introduce the notion of subset polynomial semirings and subset matrix semirings. The study of algebraic structures using subsets were recently carried out by the authors. Here we define the notion of subset row matrices, subset column matrices and subset m × n matrices. Study of this kind is developed in chapter two of this book. If we use subsets of a set X; say P(X), the power set of the set X....

Hence if P(X) is replaced by a group or a semigroup we get the subset matrix to be only a subset matrix semigroup. If …

Subset Non Associative Semirings, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book for the first time we introduce the notion of subset non associative semirings. It is pertinent to keep on record that study of non associative semirings is meager and books on this specific topic is still rare. Authors have recently introduced the notion of subset algebraic structures. The maximum algebraic structure enjoyed by subsets with two binary operations is just a semifield and semiring, even if a ring or a field is used. In case semigroups or groups are used still the algebraic structure of the subset is only a semigroup. To construct a subset non associative …

Subset Interval Groupoids, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The study of groupoids is meager and we have recently introduced the new notion of subset groupoids and have studied them. It is interesting to keep on record that interval groupoids have been studied by us in 2010. Further when the subsets of a loop are taken they also form only a subset groupoid and not a subset loop. Thus we do not have the concept of subset interval loop they only form a subset interval groupoid. Special elements like subset interval zero divisors, subset interval idempotents and subset interval units are studied. Concept of subset interval groupoid homomorphism is …