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A converse to Scheffe's theorem
... Lemma 1 below gives one set of such conditions and Theorems 1 and 2 of Section 3 verify these conditions for certain translation and scale statistics.. The statistical motivation[r] ... See full document
6
On a conjecture of Cheeger
... (strong) converse of Rademacher’s theorem has been known to be true in R since the work of Zahorski [21], where he characterized the sets E ⊂ R that are sets of non-differentiability points of some ... See full document
12
A class of principal ideal rings arising from the converse of the Chinese remainder theorem
... Note that the class Ꮿ of rings R characterized in Theorem 2.6 has some properties that are reminiscent of properties of the class of all principal ideal rings. For instance, Ꮿ is stable under the formation of ... See full document
5
g*-Closed Sets in Topological Spaces
... The converse of the above theorem need not be true in general, as seen in the following example... Proof follows from the definitions..[r] ... See full document
15
Igm - Closed Sets
... The Theorem 2.3 gives some properties of I gm − closed sets and Example 2.4.. shows that the converse need not be true.[r] ... See full document
12
g*b Homeomorphisms and Contra g*b continuous Maps in Topological Spaces
... F be a closed set in X. Then f (F ) is a g*b -closed set in Y. Since every g*b-closed set is gb-closed, f (F ) is a gb-closed set. Therefore f is a gb-closed map. Remark 3.8: The converse of the theorem 3.7 ... See full document
7
On the groups satisfying the converse of Schur's theorem
... famous theorem of Schur states that for a group G finiteness of G/Z (G) implies the finiteness of G 0 ...The converse of Schur’s theorem is an interesting problem which has been considered by some ... See full document
7
Direct and converse results in the Ba space for Jackson Matsuoka polynomials on the unit sphere
... In this paper, we introduce K-functional and modulus of smoothness of the unit sphere in the Ba space, establish their relations and obtain the direct and converse theorem of approximation in the Ba space ... See full document
13
What do aongest ncreasing ubsequence and aongest ecreasing ubsequence now bout ach ther?
... of converse of the celebrated Erd˝os-Szekeres theorem, we present a necessary and su ffi cient condition for a sequence of length n to contain a longest increasing subsequence and a longest decreasing ... See full document
8
A Converse of Minkowski's Type Inequalities
... Remark 1.2. Note that, proceeding as in the proof of Theorem 1.1, we can prove similar inequalities to 1.4 and 1.6 with n j1 i1 m instead of m i1 n j1 on the left-hand side of these inequalities. For example, such ... See full document
9
On quasi ideals and bi ideals in ternary semirings
... Proof. Let R be a right ideal, M be a lateral ideal, and L be a left ideal of S such that Q = R ∩ M ∩ L. Then, by Lemmas 3.3 and 3.7, we find that Q is a quasi-ideal of S. The converse of ... See full document
9
On completeness of quasi pseudometric spaces
... We can easily construct an example to shows that the converse of Theorem 4.2 does not hold, that is, a subspace A of an ᏹq -convergence complete quasi-pseudometric space X,d can be ᏹq -c[r] ... See full document
11
Infra Generalized b-Closed Sets in Infra Topological Space
... Conversely, let bicp(A) – A be closed. Then by theorem(4.1),bicp(A) – A does not contain any non- empty infra closed subset and since bicp(A) – A is closed subset of itself, then bicp(A) – A= . This implies that ... See full document
10
HajekArguments
... the converse Dutch Book theorem came to its rescue (even though this theorem is surprisingly ...the converse of the putative theorem (italicized in the previous paragraph) will come to ... See full document
27
Converse of Lagrange's theorem (CLT) numbers under $1000$
... A group that satisfies the converse of the Lagrange Theorem is called a CLT group. A positive integer n is called a CLT number (resp. supersolvable number) if every group of order n is a CLT group (resp. ... See full document
6
A converse theorem for double Dirichlet series and Shintani zeta functions
... our converse theorem is a refinement of that used in [3] and, as a result, the statement of the theorem is significantly ...the converse theorem, an additional set of functional ... See full document
22
2. Operators possessing properties $(gb)$ and $(gw)$
... extension to the context of B-Fredholm theory of property (b). It is proved in [15, Theorem 2.3] that an operator possessing property (gb) possesses property (b), but the converse does not hold in general ... See full document
11
A Converse Lyapunov Theorem and Robustness with Respect to Unbounded Perturbations for Exponential Dissipativity
... Proof. Suppose that 1.1 is uniformly exponentially dissipative. Then by Theorem 3.1, the perturbed system 3.1 is uniformly exponentially dissipative for any perturbation pt, x, provided P1 is satisfied with ε > ... See full document
15
A Theory of Learning with Corrupted Labels
... The preceding shows how to construct losses, we begin with a concave 1-homogeneous function and take super-gradients. Focus now turns to their convexification. Once convexified, the decision maker gains access to the ... See full document
50
A versatile proof of Fermat‟s last theorem
... For all exponents greater than 2 , the numerical relation in the form a n + b n = c n cannot exist when a,b and c are restricted to have whole integers which is called Fermat‟s Last Theorem (FLT) , but is ... See full document
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