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Some results on the Collatz problem

Ştefan Andrei, Manfred Kudlek, Radu Ştefan Niculescu
2000 Acta Informatica  
In the first part, we present some equivalent forms of this conjecture and a slight generalization of a former result from [1].  ...  Finally, we present some interesting results related to the number of "even" and "odd" branches in the Collatz's tree.  ...  We shall prove some results that will help us in our further considerations.  ... 
doi:10.1007/s002360000039 fatcat:3hyc5ji7cnf5zcxj5ztmqw4boy

Sobolev and Hölder regularity results for some singular nonhomogeneous quasilinear problems [article]

J. Giacomoni, Deepak Kumar, K. Sreenadh
2021 arXiv   pre-print
This result is completely new and of independent interest.  ...  Here they proved the existence and some Sobolev regularity results.  ...  Next, we prove Hölder continuity result for weak solution, u ∈ W 1,p loc (Ω) of problem (P), for the case β + δ ≥ 1.  ... 
arXiv:2004.06699v4 fatcat:eiijngcj4nhxdc6orff6fweoqi

The Hubbard Model: Some Rigorous Results and Open Problems [article]

Elliott Lieb
1993 arXiv   pre-print
This mini-review will explore what is known rigorously about the model and it will attempt to describe some open problems that are possibly within the range of rigorous mathematical analysis.  ...  Problem 6: Is there any residue of (5.1) when N = |Λ|? Problem 4 : 4 Does there exist some number ρ c > 0 such that lim Λ→∞ S/S max = 0 for all ρ < ρ c ?(3.12)  ...  (For a survey of this question and for some rigorous results about it see [LL2] .) The same conjecture has been made for U = 0.  ... 
arXiv:cond-mat/9311033v2 fatcat:qsm3yuvhxfb4zizqi5kfib7aou

Some results on positive solutions of a Kirchhoff type problem with indefinite conditions

Jiaqing Hu, Qiangqiang Yang
2021 SN Partial Differential Equations and Applications  
In this paper, we investigate the existence, multiplicity and asymptotic property of positive solutions for a Kirchhoff type problem with indefinite conditions.  ...  The existence, multiplicity of positive solutions are obtained by using variational method and the critical point theory, and then combing with some analytical techniques, we have the asymptotic property  ...  Thus, by the Mountain-Pass Theorem [16, 18] , we infer that c k is a positive critical value of I k . We shall discuss that the asymptotic behavior of the mountain-pass type solution.  ... 
doi:10.1007/s42985-021-00077-9 fatcat:aj6jcl6ggvgp7cy62yjuweoasu

Some results on a class of functional optimization problems [article]

David Rushing Dewhurst
2018 arXiv   pre-print
A dynamic description and statement of a partial inverse problem follow.  ...  We show that optimiziation for the incorrect probability distribution can have catastrophic results, e.g., infinite expected cost, and describe a method for continuous Bayesian update of the posterior  ...  dure described in Sec. 2.1.2 and infer the probability distribution; results are displayed in Figure 2.3.  ... 
arXiv:1804.00087v1 fatcat:4cwc3gocbvdxnelr5cx7gt3iiu

Compactness results and applications to some "zero mass" elliptic problems [article]

Antonio Azzollini, Alessio Pomponio
2006 arXiv   pre-print
In this paper we present some compactness results, showing how they can be applied in dealing with "zero mass" problems by a variational approach.  ...  In particular we use our results in two different situations: we look for complex valued solutions of a very classical elliptic equation, and we study an elliptic problem on an axially symmetric unbounded  ...  Some existence results for such a problem have been found by Benci, Grisanti & Micheletti [10, 11] and by Ghimenti & Micheletti [18] .  ... 
arXiv:math/0601410v1 fatcat:yc3galgjfrazhp7fi275mit6ai

Well-posedness and stability results for some periodic Muskat problems [article]

Bogdan-Vasile Matioc
2018 arXiv   pre-print
When neglecting surface tension effects, the Muskat problem is a fully nonlinear evolution equation and of parabolic type in the regime where the Rayleigh-Taylor condition is satisfied.  ...  We show that in the presence of surface tension effects the Muskat problem is a quasilinear parabolic problem which is well-posed in the Sobolev space H^r(S) for each r∈(2,3).  ...  In Theorem 4.2, which is the key argument in the proof of (4.2), we establish some commutator type estimates relating Φ σ,1 (τ f ) locally to some explicit Fourier multipliers.  ... 
arXiv:1804.10403v1 fatcat:uv25m562lzefbp3fhe3yhikclm

Some asymptotic results for the combination of evidence problem

I.R. Goodman
1987 Mathematical Modelling  
This function exhibits the appropriate components contributing to knowledge of the parameter, including conditions or inference rules,relating the parameter with observable characteristics or attributes  ...  Yet, often in the problem at hand, a number of observable attributes represent probabilistic concepts in the form of probability density functions.  ...  Lindley (1982). extending Savage's original argument, considered the choice of an uncertainty measure for a given situation as a decision theory problem, utilizing an additive type of loss function between  ... 
doi:10.1016/0270-0255(87)90577-x fatcat:kp4csf7purhllc6y7y3mhy3x7y

New results on some classical parabolic free-boundary problems

A. Fasano, M. Primicerio
1981 Quarterly of Applied Mathematics  
It is known that some free-boundary problems with the Cauchy data prescribed on the free boundary can be reduced to schemes of the type mentioned above, provided that suitable compatibility conditions  ...  In Sec. 4 we prove some comparison theorems for the solutions of the problems dealt with in the preceding sections.  ...  Some special topics in Stefan problems of general type.  ... 
doi:10.1090/qam/614552 fatcat:nt5xepaqrbhptokne3fd4ejpe4

Double phase problems: a survey of some recent results

Nikolaos S. Papageorgiou
2022 Opuscula Mathematica  
We review some recent results on double phase problems. We focus on the relevant function space framework, which is provided by the generalized Orlicz spaces.  ...  We also describe the basic tools and methods used to deal with double phase problems, given that there is no global regularity theory for these problems.  ...  Double phase problems: a survey of some recent results 265 This result also can be proved using a standard Moser iteration procedure.  ... 
doi:10.7494/opmath.2022.42.2.257 fatcat:5addozyv4zbxhbwfjmsxhsmehy

Monotonicity and nonexistence results for some fractional elliptic problems in the half space [article]

Mouhamed Moustapha Fall, Tobias Weth
2013 arXiv   pre-print
We study a class of fractional elliptic problems of the form u= f(u) in the half space ^N_+:={x ∈^N : x_1>0} with the complementary Dirichlet condition u ≡ 0 in ^N ∖^N_+.  ...  Our second main result is of Liouville type.  ...  We briefly explain in which sense we consider problems of type (1.1).  ... 
arXiv:1309.7230v1 fatcat:k4wf6z2x2bfehdpl7wmdodwjn4

Some new weighted compact embeddings results and existence of weak solutions for eigenvalue Robin problem [article]

Ismail Aydin, Cihan Unal
2020 arXiv   pre-print
under some appropriate conditions in the space W_a,b^1,p(.)( Ω).  ...  By applying Mountain Pass Lemma, Ekeland's and Ricceri's variational principle, Fountain Theorem, we prove the existence and multiplicity of solutions for the following Robin problem { < a r r a y > .  ...  For the multiplicity solutions of the problem (1.1), we will use some well-known results. Lemma 4. (see [11] ) Let X be a reflexive and separable Banach space.  ... 
arXiv:2011.10847v1 fatcat:72yfxxwpf5bqpllfgjmaw76y54

The Task-Dialog and Task-Presentation Mapping Problem: Some Preliminary Results [chapter]

Quentin Limbourg, Jean Vanderdonckt, Nathalie Souchon
2001 Lecture Notes in Computer Science  
Some preliminary results for solving this type of mapping problem at a high level of abstraction are provided and exemplified on some particular model representations.  ...  In this context, the mapping problem poses the challenge of defining the elements of these models and to link them into an appropriate way that reflects design options.  ...  The goal of this paper is finally to explore how these two types of mapping problems can be addressed in terms of model elements and relationships.  ... 
doi:10.1007/3-540-44675-3_14 fatcat:ma2risuw4rditgyv5zjib7ck5m

Graph intersection and uniqueness results for some nonlinear elliptic problems

A Tertikas, J.F Toland
1992 Journal of Differential Equations  
Uniqueness for problems of this type are well known when the nonlinearity f(u) g(x, u) is concave in u (see, for example, t-21).  ...  In the case of (one-dimensional) nonlinear Sturm-Liouville problems some elementary uniqueness results, not contained herein, are obtained by other means in [9] .  ... 
doi:10.1016/0022-0396(92)90047-q fatcat:c5jhm2rg3fbfjj6issd4mhn4jm

Some existence results for superlinear elliptic boundary value problems involving critical exponents

G Cerami, S Solimini, M Struwe
1986 Journal of Functional Analysis  
We shall not give a proof of this proposition, we just indicate how this claim can be achieved by combining some known facts. First note that by a result of K.  ...  Brezis and Nirenberg, in a remarkable paper [2] , were able to overcome this difficulty and proved the THEOREM Their result is based on the observation that the compactness is preserved in some energy  ... 
doi:10.1016/0022-1236(86)90094-7 fatcat:jjp5oqqhmzhj5b35byr4ab3ynm
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