1,502 research outputs found

### Efficient adaptive integration of functions with sharp gradients and cusps in n-dimensional parallelepipeds

In this paper, we study the efficient numerical integration of functions with
sharp gradients and cusps. An adaptive integration algorithm is presented that
systematically improves the accuracy of the integration of a set of functions.
The algorithm is based on a divide and conquer strategy and is independent of
the location of the sharp gradient or cusp. The error analysis reveals that for
a $C^0$ function (derivative-discontinuity at a point), a rate of convergence
of $n+1$ is obtained in $R^n$. Two applications of the adaptive integration
scheme are studied. First, we use the adaptive quadratures for the integration
of the regularized Heaviside function---a strongly localized function that is
used for modeling sharp gradients. Then, the adaptive quadratures are employed
in the enriched finite element solution of the all-electron Coulomb problem in
crystalline diamond. The source term and enrichment functions of this problem
have sharp gradients and cusps at the nuclei. We show that the optimal rate of
convergence is obtained with only a marginal increase in the number of
integration points with respect to the pure finite element solution with the
same number of elements. The adaptive integration scheme is simple, robust, and
directly applicable to any generalized finite element method employing
enrichments with sharp local variations or cusps in $n$-dimensional
parallelepiped elements.Comment: 22 page

### On weighted zero-sum sequences

Let G be a finite additive abelian group with exponent exp(G)=n>1 and let A
be a nonempty subset of {1,...,n-1}. In this paper, we investigate the smallest
positive integer $m$, denoted by s_A(G), such that any sequence {c_i}_{i=1}^m
with terms from G has a length n=exp(G) subsequence {c_{i_j}}_{j=1}^n for which
there are a_1,...,a_n in A such that sum_{j=1}^na_ic_{i_j}=0.
When G is a p-group, A contains no multiples of p and any two distinct
elements of A are incongruent mod p, we show that s_A(G) is at most $\lceil
D(G)/|A|\rceil+exp(G)-1$ if |A| is at least (D(G)-1)/(exp(G)-1), where D(G) is
the Davenport constant of G and this upper bound for s_A(G)in terms of |A| is
essentially best possible.
In the case A={1,-1}, we determine the asymptotic behavior of s_{{1,-1}}(G)
when exp(G) is even, showing that, for finite abelian groups of even exponent
and fixed rank, s_{{1,-1}}(G)=exp(G)+log_2|G|+O(log_2log_2|G|) as exp(G) tends
to the infinity. Combined with a lower bound of
$exp(G)+sum{i=1}{r}\lfloor\log_2 n_i\rfloor$, where $G=\Z_{n_1}\oplus...\oplus
\Z_{n_r}$ with 1<n_1|... |n_r, this determines s_{{1,-1}}(G), for even exponent
groups, up to a small order error term. Our method makes use of the theory of
L-intersecting set systems.
Some additional more specific values and results related to s_{{1,-1}}(G) are
also computed.Comment: 24 pages. Accepted version for publication in Adv. in Appl. Mat

### Second Order Darboux Displacements

The potentials for a one dimensional Schroedinger equation that are displaced
along the x axis under second order Darboux transformations, called 2-SUSY
invariant, are characterized in terms of a differential-difference equation.
The solutions of the Schroedinger equation with such potentials are given
analytically for any value of the energy. The method is illustrated by a
two-soliton potential. It is proven that a particular case of the periodic
Lame-Ince potential is 2-SUSY invariant. Both Bloch solutions of the
corresponding Schroedinger equation equation are found for any value of the
energy. A simple analytic expression for a family of two-gap potentials is
derived

### Training fisherwomen in fish processing

A project on training fisherwomen for their participation in rural development, sponsored by Ford Foundation (U.S.A), has been started by
the Centre for Agricultural and Rural Development Studies, T.N AU.,at the Fisheries College, Tuticorin. The project alms to select a few literate
rural women with leadership qualities for Imparting to them a training In the organisational and managerial aspects of a viable fish processing
enterprise. It also alms to assist the trained fisherwomen in organising and operating cottage industries by continued technical backing and thus
making the production units demonstration centres for the benefit of other women In the region.
The preliminary survey helped in identifying 5 candidates from each of the 3 selected villages. The pre-survey revealed the respondents'
choice of subject-areas to undergo training and their enthusiasm to learn techniques for the preparation of fish products like fish pickle and MasI
Meen. It also revealed their desire to be exposed to new products like fish wafers, fish oil, fish meal, shark fin-rays etc. The pre- and post evaluations
of the training programme helped In I) identifying training needs In the fields of marketing and financial management; II) Identifying
some low-cost technological substitutes for some of the commercial products (eg: 'Gadi' for vineger); ill) identifying the products or techniques
appreciated by the trainees and the products or techniques that received lukewarm response with reasons for such a response: Iv) Identifying the
level of managerial efficiency gained by the trainees and the kind of support required for each Individual to start cottage industries. The programme
Is being followed up by Interpersonal contacts and the co-ordinate efforts of the development departments

### Multi-Channel Inverse Scattering Problem on the Line: Thresholds and Bound States

We consider the multi-channel inverse scattering problem in one-dimension in
the presence of thresholds and bound states for a potential of finite support.
Utilizing the Levin representation, we derive the general Marchenko integral
equation for N-coupled channels and show that, unlike to the case of the radial
inverse scattering problem, the information on the bound state energies and
asymptotic normalization constants can be inferred from the reflection
coefficient matrix alone. Thus, given this matrix, the Marchenko inverse
scattering procedure can provide us with a unique multi-channel potential. The
relationship to supersymmetric partner potentials as well as possible
applications are discussed. The integral equation has been implemented
numerically and applied to several schematic examples showing the
characteristic features of multi-channel systems. A possible application of the
formalism to technological problems is briefly discussed.Comment: 19 pages, 5 figure

### Prediction of Cardiovascular disease using machine learning algorithms on healthcare data

Cardiovascular Disease (CVD) is a leading cause of death worldwide, with the potential to cause serious conditions such as heart attacks and strokes. Early assessment of CVD can significantly reduce mortality rates. In recent studies, machine learning algorithms have been applied to Electronic Health Records (EHR) to estimate risk factors for myocardial infarction. This article explores the use of various machine learning techniques on a healthcare dataset to predict a 10-year risk of future coronary heart disease (CHD). The dataset used in this study was obtained from the Framingham and Massachusetts cardiovascular study. We found that our models achieved varying levels of accuracy: 64% for logistic regression, 83% for Naïve Bayes classifier, 42% for Support Vector Machine (SVM), 65% for Random Forest, 78% for KNN classifier, and 70% for XGBOOST classifier. It is revealed that a patient with no history of heart disease may benefit from an algorithm such as Naive Bayes Classifier, while an older patient with a history of heart disease may require an algorithm such as Support Vector Machine. These factors can help guide the physician in selecting the most appropriate algorithm for each individual patient, ensuring that the diagnosis is as accurate as possible and that the treatment plan is tailored to meet the patient's unique needs

### Phase shift effective range expansion from supersymmetric quantum mechanics

Supersymmetric or Darboux transformations are used to construct local phase
equivalent deep and shallow potentials for $\ell \neq 0$ partial waves. We
associate the value of the orbital angular momentum with the asymptotic form of
the potential at infinity which allows us to introduce adequate long-distance
transformations. The approach is shown to be effective in getting the correct
phase shift effective range expansion. Applications are considered for the
$^1P_1$ and $^1D_2$ partial waves of the neutron-proton scattering.Comment: 6 pages, 3 figures, Revtex4, version to be publised in Physical
Review

### Toward a Spin- and Parity-Independent Nucleon-Nucleon Potential

A supersymmetric inversion method is applied to the singlet $^1S_0$ and
$^1P_1$ neutron-proton elastic phase shifts. The resulting central potential
has a one-pion-exchange (OPE) long-range behavior and a parity-independent
short-range part; it fits inverted data well. Adding a regularized OPE tensor
term also allows the reproduction of the triplet $^3P_0$, $^3P_1$ and $^3S_1$
phase shifts as well as of the deuteron binding energy. The potential is thus
also spin-independent (except for the OPE part) and contains no spin-orbit
term. These important simplifications of the neutron-proton interaction are
shown to be possible only if the potential possesses Pauli forbidden bound
states, as proposed in the Moscow nucleon-nucleon model.Comment: 9 pages, RevTeX, 5 ps figure

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