“…The rest of the work covers a wide range of topics, such as stochastic calculus and Markov processes, random matrices and free probability, and combinatorial optimization.…”
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“…This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations. After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic PDEs, and the associated boundary value problems. …”
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“…We obtain explicit solutions of the equation with the help of fractional calculus techniques. Using the N-fractional calculus operator N (ν) method, we derive the fractional solutions of the equation.…”
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“…No more is needed than the usual background of an undergraduate engineering, science, or mathematics program: namely calculus, differential equations, and numerical integration. …”
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“…Laplace and z­ transformations are also referred to as operational calculus, but this notion is also used in a more restricted sense to denote the operational calculus of Mikusinski. …”
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“…Mathematical tools are presented and developed as needed and only basic calculus, chemistry, and physics is assumed. Applications include atomic and molecular structure, spectroscopy, alpha decay, tunneling, and superconductivity. …”
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“…There were 46 patients with a single calculus, 4 patients with a staghorn calculus, and 6 with a caliceal calculus. …”
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“…We also found hydroureter distal to the impaction of the calculus, renal damage and severe hydronephrosis on the right side. …”
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“…In the case of the applied pi calculus, an outputted message is not explicitly expressed. …”
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“…Sequent calculus is a pervasive technique for studying logics and their properties due to the regularity of rules, proofs, and meta-property proofs across logics. …”
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“…In each variant of the [Formula: see text] -calculus, factorization and normalization are two key properties that show how results are computed. …”
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“…Cholecystectomy with the retrieval of calculus from the infundibulum and duodenum was performed with the closure of the fistulous opening. …”
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“…Incident urinary tract stone events were captured using a pre-defined collection of MedDRA terms: nephrolithiasis, renal colic, ureterolithiasis, calculus bladder, calculus urinary, calculus urethral, and nephrocalcinosis (MedDRA version 22.1). …”
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“…The aim of this book is to rebuild the tensor calculus in order to give a geometric representation of agent knowledge. …”
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“…Requiring only some background in general physics and calculus, it offers in-depth coverage of electricity and magnetism and features problems at the end of each chapter.…”
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“…The applications and concrete models from engineering and physics are often classical but the modern structure calculus was only possible since the achievements of pseudo-differential operators. …”
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“…Differential Geometry and Its Applications studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole. It mixes geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. …”
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“…In general, the emphasis is on presenting the content in a clear and straightforward way that requires only an elementary grasp of calculus, linear algebra, and Newtonian mechanics. …”
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“…But here we discuss their properties, as a group, at a level appropriate for an audience armed only with the tools of elementary calculus. This material offers an excellent excuse to display the power of calculus to reveal elegant truths that are not often seen in college classes. …”
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“…The main results are establishment of upper bounds on the elongation of deductions in cut eliminations; a proof that the length of a direct deduction of an existence theorem in the predicate calculus cannot be bounded above by an elementary function of the length of an indirect deduction of the same theorem; a complexity version of the existence property of the constructive predicate calculus; and, for certain formal systems of arithmetic, restrictions on the complexity of deductions that guarantee that the deducibility of a formula for all natural numbers in some finite set implies the deducibility of the same formula with a universal quantifier over all sufficiently large numbers.…”
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