An Elementary Proof of the Power Rule of Differentiation

Resonance ◽  
2021 ◽  
Vol 26 (11) ◽  
pp. 1585-1587
Author(s):  
Triloki Nath
Keyword(s):  
Elementary Proof ◽  
Power Rule

AN ELEMENTARY PROOF OF A THEOREM OF LEE

1991 ◽  
Vol 11 (3) ◽  
pp. 356-360 ◽  
Author(s):  
Jia'an Yan
Keyword(s):  
Elementary Proof

Sovereignty, the Corporate Religious, and Jurisdictional/Political Pluralism

2017 ◽  
Author(s):  
Jean L. Cohen
Keyword(s):  
Public Authority ◽  
Popular Sovereignty ◽  
Modern State ◽  
Public Power ◽  
Political Pluralism ◽  
Social Democratic ◽  
Liberal Democratic ◽  
Power Rule ◽  
Important Challenge ◽  
Principles Of Justice

We typically associate sovereignty with the modern state, and the coincidence of worldly powers of political rule, public authority, legitimacy, and jurisdiction with territorially delimited state authority. We are now also used to referencing liberal principles of justice, social-democratic ideals of fairness, republican conceptions of non-domination, and democratic ideas of popular sovereignty (democratic constitutionalism) for the standards that constitute, guide, limit, and legitimate the sovereign exercise of public power. This chapter addresses an important challenge to these principles: the re-emergence of theories and claims to jurisdictional/political pluralism on behalf of non-state ‘nomos groups’ within well-established liberal democratic polities. The purpose of this chapter is to preserve the key achievements of democratic constitutionalism and apply them to every level on which public power, rule, and/or domination is exercised.

scholarly journals A new elementary proof of a theorem of Minkowski

1926 ◽  
Vol 2 (3) ◽  
pp. 97-99
Author(s):  
Matsusaburô Fujiwara
Keyword(s):  
Elementary Proof

scholarly journals Antisymmetry of the Stochastical Order on all Ordered Topological Spaces

2019 ◽  
Vol 7 (1) ◽  
pp. 250-252 ◽  
Author(s):  
Tobias Fritz
Keyword(s):  
Topological Space ◽  
General Result ◽  
Elementary Proof ◽  
Short Note ◽  
Stochastic Order ◽  
Topological Spaces ◽  
Probability Measures ◽  
Ordered Topological Space ◽  
Special Cases

Abstract In this short note, we prove that the stochastic order of Radon probability measures on any ordered topological space is antisymmetric. This has been known before in various special cases. We give a simple and elementary proof of the general result.

On random divisions of a convex set

1978 ◽  
Vol 15 (3) ◽  
pp. 645-649 ◽  
Author(s):  
Svante Janson
Keyword(s):  
Elementary Proof ◽  
Convex Set ◽  
Limiting Distribution ◽  
Independent Identically Distributed ◽  
Normally Distributed

This paper gives an elementary proof that, under some general assumptions, the number of parts a convex set in Rd is divided into by a set of independent identically distributed hyperplanes is asymptotically normally distributed. An example is given where the distribution of hyperplanes is ‘too singular' to satisfy the assumptions, and where a different limiting distribution appears.

scholarly journals ON THE STABILITY OF SYZYGY BUNDLES

2011 ◽  
Vol 22 (04) ◽  
pp. 515-534 ◽  
Author(s):  
IUSTIN COANDĂ
Keyword(s):  
Projective Space ◽  
Complete Intersection ◽  
Vector Bundles ◽  
Elementary Proof ◽  
Base Point ◽  
Vector Spaces ◽  
Similar Argument ◽  
Vanishing Theorem ◽  
The Stability ◽  
Koszul Cohomology

We are concerned with the problem of the stability of the syzygy bundles associated to base-point-free vector spaces of forms of the same degree d on the projective space of dimension n. We deduce directly, from M. Green's vanishing theorem for Koszul cohomology, that any such bundle is stable if its rank is sufficiently high. With a similar argument, we prove the semistability of a certain syzygy bundle on a general complete intersection of hypersurfaces of degree d in the projective space. This answers a question of H. Flenner [Comment. Math. Helv.59 (1984) 635–650]. We then give an elementary proof of H. Brenner's criterion of stability for monomial syzygy bundles, avoiding the use of Klyachko's results on toric vector bundles. We finally prove the existence of stable syzygy bundles defined by monomials of the same degree d, of any possible rank, for n at least 3. This extends the similar result proved, for n = 2, by L. Costa, P. Macias Marques and R. M. Miro-Roig [J. Pure Appl. Algebra214 (2010) 1241–1262]. The extension to the case n at least 3 has been also, independently, obtained by P. Macias Marques in his thesis [arXiv:0909.4646/math.AG (2009)].

Elementary proof of Zeeman's theorem

1980 ◽  
Vol 19 (12) ◽  
pp. 899-903 ◽  
Author(s):  
A. J. Briginshaw
Keyword(s):  
Elementary Proof
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