College Mathematics with Applications to the Business and Social Sciences - Gulati, Bodh R. (Harper & Row, 1978)
Keywords: Mathematics; Business mathematics; Social sciences; Methodology; dept.mat; faculty_collection

Finite Mathematics: An Introduction - Gulati, Bodh R. (Harper & Row, 1975)
Keywords: Mathematics; dept.mat; faculty_collection

Geometry for Teachers - Nowlan, Robert A.; Washburn, Robert M. (1973)
Keywords: Geometry; dept.mat; faculty_collection

An isoperimetric inequality involving conformal mapping - Berlinghoff, W.P.; Reid, J.D. (Proceedings of the American Mathematical Society, 1977)
This paper characterizes quasi-pure projective (q.p.p.) and quasi-pure injective (q.p.i.) p-groups, and hence characterizes all such (abelian) torsion groups. A p-group is q.p.i. if and only if it is the direct sum of a divisible group and a torsion complete group. A nonreduced p-group is q.p.p. if and only if it is the direct sum of a divisible group and a bounded group; a reduced p-group is q.p.p. if and only if it is a direct sum of cyclic groups. © 1977 American Mathematical Society.
Keywords: Abelian group; Direct sum of cyclic groups; Pure exact sequence; Quasi-injective; Quasi-projective; Torsion complete; dept.mat

On two level symmetrical factorial designs - Kounias, E.G.; Gulati, B.R. (Annals of the Institute of Statistical Mathematics, 1972)
Keywords: dept.mat

Correction note to "on maximal (k,t)-sets" - Gulati, B.R. (Annals of the Institute of Statistical Mathematics, 1971)
Keywords: dept.mat

A study of H-spaces via left translations - Nowlan, R.A. (Pacific Journal of Mathematics, 1971)
H-spaces are examined by studying left translations, actions and a homotopy version of left translations to be called homolations. If (F, m) is an H-space, the map s: F-→FF given by s(x) = Lx, i.e. s(x) is left translation by x, is a homomorphism if and only if m is associative. In general, s is an An-map if and only if (F, m) is an An+1 space. The action r: FF × F → F is given by r(φ, x) = φ(x). The map s respects the action only of left translations. In general, s respects the action of homolations up to higherorder homotopies. Each homolation generates a family of maps to be called a homolation family. Denoting the set of all homolation families by H∞(F), s: F -→ FF factors through F → H∞(F) and this latter map is a homotopy equivalence. © 1971 Pacific Journal of Mathematics.
Keywords: dept.mat

On maximal t-linearly independent sets - Gulati, Bodh Raj; Johnson, Bruce McK.; Koehn, Uwe (Journal of Combinatorial Theory, Series A, 1973)
Consider a finite t + r − 1 dimensional projective space PG(t + r − 1, s) over a Galois field GF(s) of order s = ϱh, where ϱ and h are positive integers and ϱ is the prime characteristic of the field. A collection of k points in PG (t + r − 1, s) constitutes an L(t, k)-set if no t of them are linearly dependent. An L(t, k)-set is maximal if there exists no other L(t, k′)-set with k′ > k. The largest k for which an L(t, k)-set exists is denoted by Mt(t + r, s). K. A. Bush [3] established that Mt(t, s) = t + 1 for t ⩾ s. The purpose of this paper is to generalize this result and study Mt(t + r, s) for t, r, and s in certain relationships.
Keywords: dept.mat; information; theoretical study

An apparently algebraic property of the integers - Berlinghoff, W P (Mathematics Magazine, 1973)
Keywords: dept.mat

Maximal sets of points in finite projective space, no t-linearly dependent - Gulati, Bodh Raj; Kounias, E G (Journal of Combinatorial Theory, Series A, 1973)
Consider a finite (t + r - 1)-dimensional projective space PG(t + r - 1, s) based on the Galois field GF(s), where s is prime or power of a prime. A set of k distinct points in PG(t + r - 1, s), no t-linearly dependent, is called a (k, t)-set and such a set is said to be maximal if it is not contained in any other (k*, t)-set with k* > k. The number of points in a maximal (k, t)-set with the largest k is denoted by mt(t + r, s). Our purpose in the paper is to investigate the conditions under which two or more points can be adjoined to the basic set of Ei, i = 1, 2, ..., t + r, where Ei is a point with one in i-th position and zeros elsewhere. The problem has several applications in the theory of fractionally replicated designs and information theory. © 1973.
Keywords: dept.mat; melampolide

3 Level Symmetrical Factorial Designs and Ternary Group Codes - Gulati, BR; Kounias, EG (Sankhya-the Indian Journal of Statistics Series A, 1973)
Keywords: dept.mat; ⛔ No DOI found

More about maximal (n, r)-sets - Gulati, Bodh Raj (Information & Computation, 1972)
Consider a finite r-dimensional projective space PG(r, s) based on the Galois field GF(s) where s is prime or power of a prime. A set of n distinct points in PG(r, s), no t linearly dependent, is said to be maximal or complete if it is not contained in any other set with n* points with n* > n. The number of points in a maximal set is denoted by mt(r + 1, s). The purpose of this paper is to improve the existing bounds for m5(r + 1, s) for r ≥ 5 and s ≥ 5 (odd). The investigation of maximal sets in certain relationships of t, r and s yields parity check matrices of (r + 1) rows and n columns with elements from GF(s) satisfying the condition that no t columns are linearly dependent. This problem has applications to coding theory and also in the theory of fractionally replicated designs. © 1972 Academic Press, Inc.
Keywords: dept.mat

On maximal (k,t)-sets - Gulati, Bodh Raj (Annals of the Institute of Statistical Mathematics, 1971)
This investigation was originally motivated by the problem of determining the maximum number of points in finite n-dimensional projective space PG(n, s) based on the Galois field GF(s) of order s=ph (where p and h are positive integers and p is the prime characteristic of the field), such that no t of these chosen points are linearly dependent. A set of k distinct points in PG(n, s), no t linearly dependent, is called a (k, t)-set for k1 >k. The maximum value of k is denoted by mt (n+1, s). The purpose of this paper is to find new upper bounds for some values of n, s and t. These bounds are of importance in the experimental design and information theory problems. © 1971 Institute of Statistical Mathematics.
Keywords: dept.mat

Orthogonal arrays of strength five - Gulati, Bodh Raj (Trabajos De Estadistica Y De Investigacion Operativa, 1971)
Keywords: dept.mat

Note on the cochran Q test - Tate, Merle W; Brown, Sara M (Journal of the American Statistical Association, 1970)
Cochran’s Q test for differences between related-sample percentages or proportions has generally been incorrectly presented in secondary sources. The most common mistake results from failure to recognize that rows containing only 1’s or only 0’s, i.e., only successes or only failures, do not affect the value of Q. The F test, however, is affected by such rows. The probabilities from the χ2 and F approximations are compared with the exact probabilities in three sets of data. A rule of thumb, based on extensive study of the distribution of 0 in small samples, is given as an aid in judging when the χ2 approximation is satisfactory for practical purposes. © Taylor & Francis Group, LLC.
Keywords: dept.mat