Mathematics Faculty WorksCopyright (c) 2014 Loyola Marymount University and Loyola Law School All rights reserved.
http://digitalcommons.lmu.edu/math_fac
Recent documents in Mathematics Faculty Worksen-usWed, 10 Dec 2014 01:31:24 PST3600The Effects of 24 Weeks of Resistance Training with Simultaneous Elastic and Free Weight Loading on Muscular Performance of Novice Lifters
http://digitalcommons.lmu.edu/math_fac/17
http://digitalcommons.lmu.edu/math_fac/17Mon, 08 Dec 2014 22:53:32 PST
The purpose of this investigation was to assess the effectiveness of variable resistance as provided through elastic plus free weight techniques in college aged males and females. Twenty novice lifters were randomly assigned to a traditional free weight only (6 males and 5 females) or elastic band plus free weight group (5 males and 5 females) and 9 more normally active controls (5 males and 4 females), were recruited to maintain normal activity for the duration of the study. No differences existed between control, free weight and elastic band at baseline for age, body height, body mass, body mass index, and body fat percentage. One-repetition maximums were performed for squat and bench press while both strength and power were assessed using isokinetic dynamometry. Elastic groups and free-weight groups completed 24 weeks of whole body, periodized, high intensity resistance (65-95% of one-repetition maximum) training three times/week. Training programs were identical except that the elastic group trained the barbell squat, bench press and stiff-legged deadlift with 20-35% of their total prescribed training loads coming from band resistance (assessed at the top of the range of motion) with the remainder from free weight resistance. A mixed-model analysis revealed that peak torque, average power and one-repetition maximums for squat were significantly greater after training for the elastic group compared to the control (p<0.05). In addition, the free weight group also showed significantly greater improvements over the control in peak torque and one-repetition maximums for squat and bench press. No significant differences were observed between the elastic band and free weight groups. Combined variable elastic band plus free weight exercises are effective at increasing strength and power similar to free-weights alone in novice college aged males and females. However, due to complexity in set-up and load assignment elastic adoption by novice lifters in an unsupervised situation is not advised.
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Robert RovettiComputational Modeling and Numerical Methods for Spaciotemporal Calcium Cycling in Ventricular Myocytes
http://digitalcommons.lmu.edu/math_fac/16
http://digitalcommons.lmu.edu/math_fac/16Mon, 08 Dec 2014 21:45:36 PST
Intracellular calcium (Ca) cycling dynamics in cardiac myocytes is regulated by a complex network of spatially distributed organelles, such as sarcoplasmic reticulum (SR), mitochondria, and myofibrils. In this study, we present a mathematical model of intracellular Ca cycling and numerical and computational methods for computer simulations. The model consists of a coupled Ca release unit (CRU) network, which includes a SR domain and a myoplasm domain. Each CRU contains 10 L-type Ca channels and 100 ryanodine receptor channels, with individual channels simulated stochastically using a variant of Gillespie’s method, modified here to handle time-dependent transition rates. Both the SR domain and the myoplasm domain in each CRU are modeled by 5 × 5 × 5 voxels to maintain proper Ca diffusion. Advanced numerical algorithms implemented on graphical processing units were used for fast computational simulations. For a myocyte containing 100 × 20 × 10 CRUs, a 1-s heart time simulation takes about 10 min of machine time on a single NVIDIA Tesla C2050. Examples of simulated Ca cycling dynamics, such as Ca sparks, Ca waves, and Ca alternans, are shown.
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Robert RovettiEffects of visual, auditory, and kinesthetic imagery interventions on dancers’ Plié Arabesques.
http://digitalcommons.lmu.edu/math_fac/15
http://digitalcommons.lmu.edu/math_fac/15Mon, 08 Dec 2014 21:45:27 PST
The goal of this study was to examine the influence of visual, auditory, and kinesthetic delivery modes of Franklin Method images (anatomical bone rhythms, metaphorical image, and tactile aid, respectively) on the performance of college dancers’ Plié Arabesques by assessing its influence on three measures: plié depth; maintenance of rotation; and simultaneous use of hip, knee, and ankle (Tri-fold). Eighteen participants performed a series of Plié Arabesques during three visits over a period of two months; at each visit, pliés were performed before and after an image intervention, and the change in mean Likert scale rating was calculated for each measure. In 130 out of 162 ratings, Plié Arabesque scores were higher following the image interventions. Based on t-test comparisons, the visual mode produced significant positive improvement for all three measures (p≤0.001 for each), while the kinesthetic mode produced increased ratings for the Rotation (p=0.012) and Tri-fold (p=0.019) measures. The auditory mode was associated with increased ratings in the Tri-fold measure only (p<0.001). One-way ANOVA suggests no one image modality performed significantly better or worse than the others for the Rotation or Tri-fold; however, the Visual mode did have a noticeably stronger positive effect for Plié (p=0.003). We also explored possible relationships between years of experience dancing and preferred learning styles (as measured by the VARK, VAK, and MIQ-R assessment tools) to performance outcomes, and observed highly varied relationships but no definitive pattern of correlations. Dancers’ anecdotal comments about their perceived success with the imagery were qualitatively compared to their performance outcomes. This exploratory study suggests that Franklin Method imagery employing various delivery modalities can be successfully used to improve aspects of the Plié Arabesque, although some modalities may have a stronger effect. We offer recommendations for both the pedagogical application of Franklin Method based on aspects of technique as well as design of future studies to further explore learning styles and other personal aspects of imagery abilities
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Robert Rovetti et al.Macroscopic Consequences of Calcium Signaling in Microdomains: A First-Passage-Time Approach
http://digitalcommons.lmu.edu/math_fac/14
http://digitalcommons.lmu.edu/math_fac/14Mon, 08 Dec 2014 20:28:54 PST
Calcium (Ca) plays an important role in regulating various cellular processes. In a variety of cell types, Ca signaling occurs within microdomains where channels deliver localized pulses of Ca activating a nearby collection of Ca-sensitive receptors. The small number of channels involved ensures that the signaling process is stochastic. The aggregate response of several thousand of these microdomains yields a whole-cell response which dictates the cell behavior. Here, we study the statistical properties of a population of these microdomains in response to a trigger signal. We use a first-passage-time approach to show analytically how Ca release in the whole cell depends on properties of Ca channels within microdomains. Using these results we explain for the first time the underlying mechanism for the graded relationship between Ca influx and Ca release in cardiac cells.
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Robert RovettiPeriod-Doubling Bifurcation in an Array of Coupled Stochastically Excitable Elements Subjected to Global Periodic Forcing
http://digitalcommons.lmu.edu/math_fac/13
http://digitalcommons.lmu.edu/math_fac/13Mon, 08 Dec 2014 20:18:17 PST
The collective behaviors of coupled, stochastically excitable elements subjected to global periodic forcing are investigated numerically and analytically. We show that the whole system undergoes a period-doubling bifurcation as the driving period decreases, while the individual elements still exhibit random excitations. Using a mean-field representation, we show that this macroscopic bifurcation behavior is caused by interactions between the random excitation, the refractory period, and recruitment (spatial cooperativity) of the excitable elements.
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Robert RovettiA New Proof of a Theorem of Phan
http://digitalcommons.lmu.edu/math_fac/12
http://digitalcommons.lmu.edu/math_fac/12Tue, 07 Feb 2012 14:41:21 PST
We apply diagram geometry and amalgam techniques to give a new proof of a theorem of K.-W. Phan, characterizing the special unitary group as a group generated by certain systems of subgroups SU(2, q(2)).
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Curtis Bennett et al.Sufficient Conditions for an Operator-Valued Feynman-Kac Formula
http://digitalcommons.lmu.edu/math_fac/11
http://digitalcommons.lmu.edu/math_fac/11Tue, 07 Feb 2012 14:41:20 PST
Let E be a locally compact, second countable Hausdorff space and let X(t) be a Markov process with state space E. Sufficient conditions are given for the existence of a solution to the initial value problem, ∂u/∂t,=Au + V(x) * u, u(0) = f, where A is the infinitesimal generator of the process X on a certain Banach space and for each x ∈ E, V(x) is the infinitesimal generator of a C_{0} contraction semigroup on another Banach space.
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Michael D. GradyPseudoprime L-Ideals in a Class of F-Rings
http://digitalcommons.lmu.edu/math_fac/10
http://digitalcommons.lmu.edu/math_fac/10Tue, 07 Feb 2012 14:41:19 PST
In a commutative f-ring, an l-ideal I is called pseudoprime if ab = 0 implies a ∈ I or b ∈ I, and is called square dominated if for every a ∈ I, |a| ≤ x^{2} for some x ∈ A such that x^{2} ∈ I. Several characterizations of pseudoprime l-ideals are given in the class of commutative semiprime f-rings in which minimal prime l-ideals are square dominated. It is shown that the hypothesis imposed on the f-rings, that minimal prime l-ideals are square dominated, cannot be omitted or generalized.
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Suzanne LarsonSums of Semiprime, Z, and D L-Ideals in a Class of F-Rings
http://digitalcommons.lmu.edu/math_fac/9
http://digitalcommons.lmu.edu/math_fac/9Tue, 07 Feb 2012 14:41:17 PST
In this paper it is shown that there is a large class of f-rings in which the sum of any two semiprime i-ideals is semiprime. This result is used to give a class of commutative f-rings with identity element in which the sum of any two z-ideals which are i-ideals is a z-ideal and the sum of any two d-ideals is a d-ideal.
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Suzanne LarsonLattice-Ordered Algebras That Are Subdirect Products of Valuation Domains
http://digitalcommons.lmu.edu/math_fac/8
http://digitalcommons.lmu.edu/math_fac/8Tue, 07 Feb 2012 14:41:16 PST
An f-ring (i.e., a lattice-ordered ring that is a subdirect product pf totally ordered rings) A is called an SV-ring if AIP is a valuation domain for every prime ideal P of A. If M is a maximal e-ideal of A,then the rank of A at M is the number of minimal prime ideals of A contained in M, rank of A is the sup of the ranks of A at each of its maximal e-ideals. If the latter is a positive integer, then A is said to have finite rank, and if A = C(X) is the ring of all real-valued continuous functions on a Tychonoff space, the rank of X is defined to be the rank of the f-ring C(X),and X is called an SV-space if C(X) is an SV-ring. X has finite rank k iff k is the maximal number of painwise disjoint cozero sets with a point common to all of their closures. In general f-rings these two concepts are unrelated, but if ii is uniformly complete (in particular, if A = C(X)) then if A is an SV-ring then it has finite rank. Showing that this latter holds makes use of the theory of finite-valued lattice-ordered (abelian) groups. These two kinds of rings are investigated with an emphasis on the uniformly complete case. Fairly powerful machinery seems to have to be used, and even then, we do not know if there is a compact space X of finite rank that fails to be an SV-space.
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Melvin Henriksen et al.Cohomology of Polynomials Under an Irrational Rotation
http://digitalcommons.lmu.edu/math_fac/7
http://digitalcommons.lmu.edu/math_fac/7Tue, 07 Feb 2012 14:41:15 PST
A new description of cohomology of functions under an irrational rotation is given in terms of symmetry properties of the functions on subintervals of [0, 1]. This description yields a method for passing information about the cohomology classes for a given irrational to the cohomology classes for an equivalent irrational.
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Lawrence W. Baggett et al.On Functions That Are Trivial Cocycles for a Set of Irrationals. II
http://digitalcommons.lmu.edu/math_fac/6
http://digitalcommons.lmu.edu/math_fac/6Tue, 07 Feb 2012 14:41:14 PST
Two results are obtained about the topological size of the set of irrationals for which a given function is a trivial cocycle. An example of a continuous function which is a coboundary with non-L(1) cobounding function is constructed.
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Lawrence W. Baggett et al.The Growth of Valuations on Rational Function Fields in Two Variables
http://digitalcommons.lmu.edu/math_fac/5
http://digitalcommons.lmu.edu/math_fac/5Tue, 07 Feb 2012 14:41:13 PST
Given a valuation on the function field k( x; y), we examine the set of images of nonzero elements of the underlying polynomial ring k[ x; y] under this valuation. For an arbitrary field k, a Noetherian power series is a map z : Q --> k that has Noetherian (i.e., reverse well-ordered) support. Each Noetherian power series induces a natural valuation on k( x; y). Although the value groups corresponding to such valuations are well-understood, the restrictions of the valuations to underlying polynomial rings have yet to be characterized. Let Lambda(n) denote the images under the valuation v of all nonzero polynomials f is an element of k[ x; y] of at most degree n in the variable y. We construct a bound for the growth of Lambda(n) with respect to n for arbitrary valuations, and then specialize to valuations that arise from Noetherian power series. We provide a sufficient condition for this bound to be tight.
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Edward Mosteig et al.A Map on the Space of Rational Functions
http://digitalcommons.lmu.edu/math_fac/4
http://digitalcommons.lmu.edu/math_fac/4Tue, 07 Feb 2012 14:41:12 PST
We describe dynamical properties of a map defined on the space of rational functions. The fixed points of F are classified and the long time behavior of a subclass is described in terms of Eulerian polynomials.
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G. Boros et al.Computing Boundary Slopes of 2-Bridge Links
http://digitalcommons.lmu.edu/math_fac/3
http://digitalcommons.lmu.edu/math_fac/3Tue, 07 Feb 2012 14:41:10 PST
We describe an algorithm for computing boundary slopes of 2-bridge links. As an example, we work out the slopes of the links obtained by 1/k surgery on one component of the Borromean rings. A table of all boundary slopes of all 2-bridge links with 10 or less crossings is also included.
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Jim Hoste et al.A Multiple-Precision Division Algorithm
http://digitalcommons.lmu.edu/math_fac/2
http://digitalcommons.lmu.edu/math_fac/2Tue, 07 Feb 2012 14:41:08 PST
The classical algorithm for multiple-precision division normalizes digits during each step and sometimes makes correction steps when the initial guess for the quotient digit turns out to be wrong. A method is presented that runs faster by skipping most of the intermediate normalization and recovers from wrong guesses without separate correction steps.
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David M. SmithEfficient Multiple-Precision Evaluation of Elementary Functions
http://digitalcommons.lmu.edu/math_fac/1
http://digitalcommons.lmu.edu/math_fac/1Tue, 07 Feb 2012 14:41:07 PST
Let M(t) denote the time required to multiply two t-digit numbers using base b arithmetic. Methods are presented for computing the elementary functions in O(t^{1/3} M(t)) time.
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David M. Smith