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Basu
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#	Item
301	A HELLY-TYPE THEOREM FOR SEMI-MONOTONE SETS AND MONOTONE MAPS SAUGATA BASU, ANDREI GABRIELOV, AND NICOLAI VOROBJOV Abstract. We consider sets and maps defined over an o-minimal structure over the reals, such as real semi Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2012-02-06 10:58:55 Monotonic function Convex function Continuous function Mathematical analysis Mathematics Order theory
302	ON HOMOTOPY TYPES OF LIMITS OF SEMI-ALGEBRAIC SETS AND ADDITIVE COMPLEXITY OF POLYNOMIALS SAL BARONE AND SAUGATA BASU Abstract. We prove that the number of homotopy types of limits of oneparameter semi-algebraic families Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2011-02-02 17:01:53 Mathematical structures Field theory Algebraic structures Algebraic geometry Homotopy group Homotopy theory Topology Homotopy Polynomial Abstract algebra Mathematics Algebra
303	MONOTONE FUNCTIONS AND MAPS arXiv:1201.0491v1 [math.LO] 2 Jan 2012 SAUGATA BASU, ANDREI GABRIELOV, AND NICOLAI VOROBJOV Abstract. In [1] we deﬁned semi-monotone sets, as open bounded sets, deﬁnable in an o-minimal s Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2012-01-04 13:06:52 Real analysis Homeomorphisms Functional analysis Monotonic function Continuous function Semi-continuity Topological property Monotone Monotone convergence theorem Mathematical analysis Mathematics Order theory
304	A SHARPER ESTIMATE ON THE BETTI NUMBERS OF SETS DEFINED BY QUADRATIC INEQUALITIES SAUGATA BASU AND MICHAEL KETTNER Abstract. In this paper we consider the problem of bounding the Betti numbers, bi (S), of a semi-algebrai Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:31:16 Quadratic forms Algebraic topology Betti number Topological graph theory Algebraic geometry Real algebraic geometry Algebraic variety Weil conjectures Algebra Mathematics Abstract algebra
305	BOUNDING THE EQUIVARIANT BETTI NUMBERS AND COMPUTING ´ CHARACTERISTIC OF THE GENERALIZED EULER-POINCARE SYMMETRIC SEMI-ALGEBRAIC SETS SAUGATA BASU AND CORDIAN RIENER Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2014-01-17 21:15:39 Algebraic topology Algebraic geometry Field theory Polynomials Betti number Homogeneous polynomial Algebraic variety Symmetric polynomial Real algebraic geometry Abstract algebra Algebra Mathematics
306	ON PROJECTIONS OF SEMI-ALGEBRAIC SETS DEFINED BY FEW QUADRATIC INEQUALITIES SAUGATA BASU AND THIERRY ZELL Abstract. Let S ⊂ Rk+m be a compact semi-algebraic set defined by P1 ≥ 0, . . . , P` ≥ 0, where Pi ∈ R[X1 Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:36:46 Algebraic topology Homological algebra Homology theory Algebraic geometry Group theory Betti number Sheaf Spectral sequence Cohomology Abstract algebra Algebra Mathematics
307	BOUNDING THE NUMBER OF STABLE HOMOTOPY TYPES OF A PARAMETRIZED FAMILY OF SEMI-ALGEBRAIC SETS DEFINED BY QUADRATIC INEQUALITIES SAUGATA BASU AND MICHAEL KETTNER Abstract. We prove a nearly optimal bound on the number of s Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:36:03 Homotopy Algebraic geometry CW complex Algebraic topology Freudenthal suspension theorem Homotopy category Topology Homotopy theory Abstract algebra
308	POLYNOMIAL HIERARCHY, BETTI NUMBERS AND A REAL ANALOGUE OF TODA’S THEOREM SAUGATA BASU AND THIERRY ZELL Abstract. Toda [36] proved in 1989 that the (discrete) polynomial time hierarchy, PH, is contained in the class P# Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:44:12 Field theory Real algebraic geometry Algebraic geometry Real closed field Betti number Polynomial Algebraic variety Field Semialgebraic set Abstract algebra Mathematics Algebra
309	AN ASYMPTOTICALLY TIGHT BOUND ON THE NUMBER OF SEMI-ALGEBRAICALLY CONNECTED COMPONENTS OF REALIZABLE SIGN CONDITIONS SAUGATA BASU, RICHARD POLLACK, AND MARIE-FRANC ¸ OISE ROY Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:35:24 Algebraic topology Field theory Betti number Topological graph theory Algebraically closed field Holomorphic functional calculus Mathematics Abstract algebra Algebra
310	ON THE PROSPECTS FOR ENDLESS FERTILITY DECLINE IN SOUTH ASIA Alaka Malwade Basu∗ In the demographic literature, the semantics of fertility decline have led to some interesting confusion. In particular, confusion has be Add to Reading List Source URL: www.un.org Language: English - Date: 2002-10-02 20:10:40 Human geography Science Total fertility rate Sub-replacement fertility Natural fertility Demographics of the United States Population momentum Fertility-development controversy Demography Population Fertility

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