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Some results on the Collatz problem

2000
*
Acta Informatica
*

In the first part, we present

doi:10.1007/s002360000039
fatcat:3hyc5ji7cnf5zcxj5ztmqw4boy
*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. ...##
###
Sobolev and Hölder regularity results for some singular nonhomogeneous quasilinear problems
[article]

2021
*
arXiv
*
pre-print

This

arXiv:2004.06699v4
fatcat:eiijngcj4nhxdc6orff6fweoqi
*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. ...##
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The Hubbard Model: Some Rigorous Results and Open Problems
[article]

1993
*
arXiv
*
pre-print

This mini-review will explore what is known rigorously about the model and it will attempt to describe

arXiv:cond-mat/9311033v2
fatcat:qsm3yuvhxfb4zizqi5kfib7aou
*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. ...##
###
Some results on positive solutions of a Kirchhoff type problem with indefinite conditions

2021
*
SN Partial Differential Equations and Applications
*

In this paper, we investigate the existence, multiplicity and asymptotic property of positive solutions for a Kirchhoff

doi:10.1007/s42985-021-00077-9
fatcat:aj6jcl6ggvgp7cy62yjuweoasu
*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. ...##
###
Some results on a class of functional optimization problems
[article]

2018
*
arXiv
*
pre-print

A dynamic description and statement of a partial inverse

arXiv:1804.00087v1
fatcat:4cwc3gocbvdxnelr5cx7gt3iiu
*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. ...##
###
Compactness results and applications to some "zero mass" elliptic problems
[article]

2006
*
arXiv
*
pre-print

In this paper we present

arXiv:math/0601410v1
fatcat:yc3galgjfrazhp7fi275mit6ai
*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] . ...##
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Well-posedness and stability results for some periodic Muskat problems
[article]

2018
*
arXiv
*
pre-print

When neglecting surface tension effects, the Muskat

arXiv:1804.10403v1
fatcat:uv25m562lzefbp3fhe3yhikclm
*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. ...##
###
Some asymptotic results for the combination of evidence problem

1987
*
Mathematical Modelling
*

This function exhibits the appropriate components contributing to knowledge of the parameter, including conditions or

doi:10.1016/0270-0255(87)90577-x
fatcat:kp4csf7purhllc6y7y3mhy3x7y
*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 ...##
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New results on some classical parabolic free-boundary problems

1981
*
Quarterly of Applied Mathematics
*

It is known that

doi:10.1090/qam/614552
fatcat:nt5xepaqrbhptokne3fd4ejpe4
*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*. ...##
###
Double phase problems: a survey of some recent results

2022
*
Opuscula Mathematica
*

We review

doi:10.7494/opmath.2022.42.2.257
fatcat:5addozyv4zbxhbwfjmsxhsmehy
*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. ...##
###
Monotonicity and nonexistence results for some fractional elliptic problems in the half space
[article]

2013
*
arXiv
*
pre-print

We study a class of fractional elliptic

arXiv:1309.7230v1
fatcat:k4wf6z2x2bfehdpl7wmdodwjn4
*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). ...##
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Some new weighted compact embeddings results and existence of weak solutions for eigenvalue Robin problem
[article]

2020
*
arXiv
*
pre-print

under

arXiv:2011.10847v1
fatcat:72yfxxwpf5bqpllfgjmaw76y54
*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. ...##
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The Task-Dialog and Task-Presentation Mapping Problem: Some Preliminary Results
[chapter]

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. ...

##
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Graph intersection and uniqueness results for some nonlinear elliptic problems

1992
*
Journal of Differential Equations
*

Uniqueness for

doi:10.1016/0022-0396(92)90047-q
fatcat:c5jhm2rg3fbfjj6issd4mhn4jm
*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] . ...##
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Some existence results for superlinear elliptic boundary value problems involving critical exponents

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

doi:10.1016/0022-1236(86)90094-7
fatcat:jjp5oqqhmzhj5b35byr4ab3ynm
*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 ...
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