A Negative Solution to Ono’s Problem P52: Existence and Disjunction Properties in Intermediate Predicate Logics

2021 ◽  
pp. 319-337
Author(s):  
Nobu-Yuki Suzuki
Keyword(s):  
Negative Solution ◽  
Intermediate Predicate Logics

On the equation ut = ∆uα + uβ

1993 ◽  
Vol 123 (2) ◽  
pp. 373-390 ◽  
Author(s):  
Yuan-Wei Qi
Keyword(s):  
Dynamical System ◽  
Blow Up ◽  
Uniqueness Result ◽  
Fast Diffusion ◽  
Negative Solution ◽  
Fast Diffusion Equation ◽  
Infinite Dimensional ◽  
The Cauchy Problem ◽  
Dimensional Dynamical System ◽  
Infinite Dimensional Dynamical System

SynopsisThe Cauchy problem of ut, = ∆uα + uβ, where 0 < α < l and α>1, is studied. It is proved that if 1< β<α + 2/n then every nontrivial non-negative solution is not global in time. But if β>α+ 2/n there exist both blow-up solutions and global positive solutions which decay to zero as t–1/(β–1) when t →∞. Thus the famous Fujita result on ut = ∆u + up is generalised to the present fast diffusion equation. Furthermore, regarding the equation as an infinite dimensional dynamical system on Sobolev space W1,s (W2.s) with S > 1, a non-uniqueness result is established which shows that there exists a positive solution u(x, t) with u(., t) → 0 in W1.s (W2.s) as t → 0.

scholarly journals Sign-changing and multiple solutions for thep-Laplacian

2002 ◽  
Vol 7 (12) ◽  
pp. 613-625 ◽  
Author(s):  
Siegfried Carl ◽  
Kanishka Perera
Keyword(s):  
Positive Solution ◽  
Multiple Solutions ◽  
Negative Solution ◽  
Jumping Nonlinearities

We obtain a positive solution, a negative solution, and a sign-changing solution for a class ofp-Laplacian problems with jumping nonlinearities using variational and super-subsolution methods.

Semilinear Integrodifferential Problems With Non-Symmetric Kernels Via Mountain-Pass Techniques

2005 ◽  
Vol 5 (1) ◽  
Author(s):  
Silvia Mataloni ◽  
Michele Matzeu
Keyword(s):  
Iterative Scheme ◽  
Integrodifferential Equations ◽  
Mountain Pass ◽  
Negative Solution

AbstractIntegrodifferential equations with non-symmetric kernels are considered. The existence of a non-negative solution is stated through an iterative scheme and a mountain-pass technique.

scholarly journals On the Non-Negative Radial Solutions of the Two Dimensional Bratu Equation

2021 ◽  
Vol 45 (02) ◽  
pp. 275-288
Author(s):  
MBE KOUA CHRISTOPHE NDJATCHI ◽  
PANAYOTIS VYRIDIS ◽  
JUAN MARTÍNEZ ◽  
J. JUAN ROSALES
Keyword(s):  
Finite Difference ◽  
Boundary Value Problem ◽  
Theoretical Result ◽  
Theoretical Method ◽  
Parameter Estimate ◽  
Two Dimensional ◽  
Negative Solution ◽  
Radial Solutions ◽  
Seidel Method ◽  
Bratu Equation

In this paper, we study the boundary value problem on the unit circle for the Bratu’s equation depending on the real parameter μ. From the parameter estimate, the existence of non-negative solution is set. A numerical method is suggested to justify the theoretical result. It is a combination of the adaptation of finite difference and Gauss-Seidel method allowing us to obtain a good approximation of μc, with respect to the exact theoretical method μc = λ = 5.7831859629467.

Church’s theorem and the decision problem

2018 ◽  
Author(s):  
Rohit Parikh
Keyword(s):  
Decision Problem ◽  
Combinatorial Problem ◽  
Order Logic ◽  
First Order Logic ◽  
Negative Solution ◽  
Great Contribution ◽  
Solvable Problem ◽  
First Order ◽  
Mathematical Definition ◽  
Definition Of

Church’s theorem, published in 1936, states that the set of valid formulas of first-order logic is not effectively decidable: there is no method or algorithm for deciding which formulas of first-order logic are valid. Church’s paper exhibited an undecidable combinatorial problem P and showed that P was representable in first-order logic. If first-order logic were decidable, P would also be decidable. Since P is undecidable, first-order logic must also be undecidable. Church’s theorem is a negative solution to the decision problem (Entscheidungsproblem), the problem of finding a method for deciding whether a given formula of first-order logic is valid, or satisfiable, or neither. The great contribution of Church (and, independently, Turing) was not merely to prove that there is no method but also to propose a mathematical definition of the notion of ‘effectively solvable problem’, that is, a problem solvable by means of a method or algorithm.

scholarly journals A Novel Technique to Solve the Fuzzy System of Equations

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 850
Author(s):  
Nasser Mikaeilvand ◽  
Zahra Noeiaghdam ◽  
Samad Noeiaghdam ◽  
Juan J. Nieto
Keyword(s):  
Linear System ◽  
Fuzzy Number ◽  
Fuzzy System ◽  
Linear Equations ◽  
Second Step ◽  
Negative Solution ◽  
System Of Linear Equations ◽  
Vector Solution ◽  
Novel Technique ◽  
Fuzzy Linear System

The aim of this research is to apply a novel technique based on the embedding method to solve the n × n fuzzy system of linear equations (FSLEs). By using this method, the strong fuzzy number solutions of FSLEs can be obtained in two steps. In the first step, if the created n × n crisp linear system has a non-negative solution, the fuzzy linear system will have a fuzzy number vector solution that will be found in the second step by solving another created n × n crisp linear system. Several theorems have been proved to show that the number of operations by the presented method are less than the number of operations by Friedman and Ezzati’s methods. To show the advantages of this scheme, two applicable algorithms and flowcharts are presented and several numerical examples are solved by applying them. Furthermore, some graphs of the obtained results are demonstrated that show the solutions are fuzzy number vectors.

On the Square Subgroup of a Mixed SI-Group

2018 ◽  
Vol 61 (1) ◽  
pp. 295-304 ◽  
Author(s):  
R. R. Andruszkiewicz ◽  
M. Woronowicz
Keyword(s):  
Abelian Group ◽  
Quotient Group ◽  
Abelian Groups ◽  
Additive Group ◽  
Negative Solution ◽  
New Class ◽  
Free Rank ◽  
Torsion Free Rank ◽  
Torsion Free ◽  
Group Modulo

AbstractThe relation between the structure of a ring and the structure of its additive group is studied in the context of some recent results in additive groups of mixed rings. Namely, the notion of the square subgroup of an abelian group, which is a generalization of the concept of nil-group, is considered mainly for mixed non-splitting abelian groups which are the additive groups only of rings whose all subrings are ideals. A non-trivial construction of such a group of finite torsion-free rank no less than two, for which the quotient group modulo the square subgroup is not a nil-group, is given. In particular, a new class of abelian group for which an old problem posed by Stratton and Webb has a negative solution, is indicated. A new, far from obvious, application of rings in which the relation of being an ideal is transitive, is obtained.

scholarly journals A NOVEL METHOD BASED ON THE TIKHONOV FUNCTIONAL FOR NON-NEGATIVE SOLUTION OF A SYSTEM OF LINEAR EQUATIONS WITH NON-NEGATIVE COEFFICIENTS

2014 ◽  
Vol 11 (05) ◽  
pp. 1350071 ◽  
Author(s):  
FIKS ILYA
Keyword(s):  
Linear Equations ◽  
Negative Solution ◽  
System Of Linear Equations ◽  
Novel Method ◽  
Accuracy And Stability

We propose a novel method for a solution of a system of linear equations with the non-negativity condition. The method is based on the Tikhonov functional and has better accuracy and stability than other well-known algorithms.

Intermediate predicate logics determined by ordinals

1990 ◽  
Vol 55 (3) ◽  
pp. 1099-1124 ◽  
Author(s):  
Pierluigi Minari ◽  
Mitio Takano ◽  
Hiroakira Ono
Keyword(s):  
Predicate Logic ◽  
The Other ◽  
Constant Domain ◽  
Kripke Frames ◽  
Other Hand ◽  
Countable Ordinal ◽  
Intermediate Predicate Logics ◽  
Regular Ordinal

AbstractFor each ordinal α > 0, L(α) is the intermediate predicate logic characterized by the class of all Kripke frames with the poset α and with constant domain. This paper will be devoted to a study of logics of the form L(α). It will be shown that for each uncountable ordinal of the form α + η with a finite or a countable η(> 0), there exists a countable ordinal of the form β + η such that L(α + η) = L(β + η). On the other hand, such a reduction of ordinals to countable ones is impossible for a logic L(α) if α is an uncountable regular ordinal. Moreover, it will be proved that the mapping L is injective if it is restricted to ordinals less than ωω, i.e. α ≠ β implies L(α) ≠ L(β) for each ordinal α, β ≤ ωω.

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