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### Finding models through graph saturation [article]

Sebastiaan J. C. Joosten
2018 arXiv   pre-print
We give a procedure that can be used to automatically satisfy invariants of a certain shape.  ...  We prove correctness of the procedure. Moreover, we show the corresponding decision problem to be undecidable. This confirms a conjecture previously stated by the author.  ...  Part of the research presented in this paper was performed at the University of Innsbruck, Austria, supported by the Austrian Science Fund (FWF) project Y757.  ...

### Finding models through graph saturation

Sebastiaan J.C. Joosten
2018 Journal of Logical and Algebraic Methods in Programming
We give a procedure that can be used to automatically satisfy invariants of a certain shape.  ...  This is an accepted preprint, which will be published in the Journal of Logical and Algebraic Methods in Programming (JLAMP).  ...  Note that ( , ) is the graph rule drawn in Graph 1 = ({ , , }, {0, 1, 2, 3}, {( , 0, 1), ( , 0, 0), ( , 2, 3), ( , 2, 2)}), consisting of two disjunctive copies of 1 , is a least consequence graph too  ...

### On Weak-BCC-Algebras

Janus Thomys, Xiaohong Zhang
2013 The Scientific World Journal
A -nilradical [ ; ] of a nonempty subset of a weak-BCC-algebra is nonempty if and only if contains at least one element ∈ ( ). Proof.  ...  From the proof of Theorem 16, it follows that 0 * = 0 * for every ∈ ( ) and any positive . So, ∈ [ ; ] if and only if 0 * ∈ . The last means that 0 * ∈ ∩ ( ) because ( ) is a subalgebra of .  ...  But there are only two weak-BCC-algebras of order four which are not isomorphic: * 0 1 2 3 0 0 0 2 2 1 1 0 2 2 2 2 2 0 0 3 3 3 1 0 (4) * 0 1 2 3 0 0 0 2 2 1 1 0 3 3 2 2 2 0 0 3 3 3 1 0 (5) 1 0 2 3 (6)  ...

### Weak values could reveal the hidden effects of quantum interactions [article]

Miao Zhang
2015 arXiv   pre-print
From this point of view, the post-selection induced weak value could be one of the feasible methods for measuring the weak interaction, since the standard measurement does not work.  ...  Additionally, we employ the system of trapped ions to simulate the weak measurement and calculate relevant results without the frequently-used weak interaction approximation.  ...  By the so-called sideband excitation [26, 27] , this qubit can be coupled to the center-of-mass (CM) motion of the two vibrational ions, and consequently the desirable Hamiltonian of (16) could be realized  ...

### Modular annihilator \$Asp{ast} \$-algebras

B. J. Tomiuk
(ii) Suppose / is a nonzero two-sided ideal of 3t. Then, by (i), A 0/^(0). Thus J=A n lis a nonzero two-sided ideal of ^4 and, by the semi-simplicity of A, AJÏ£(0). Hence AI^(0).  ...  Then ezz*e=Àe, A^O in C This shows that e e /which clearly contradicts the fact that A n /= (0). Hence AI-(0) and consequently %I= (0). Since 3t is semi-simple, we must have 7=(0).  ...  Hence, by the weak (^-property, ||xa|| 2 =0 which implies that xa=0 and consequently that JC/=(0). It follows now that xS A =(0) and hence that x=0 since l A (S A )=(0). Applying Proof. (i)-*(ii).  ...

### Existence and multiplicity results to Neumann problems for elliptic equations involving the p-Laplacian

Gabriele Bonanno, Angela Sciammetta
2012 Journal of Mathematical Analysis and Applications
In this paper, existence results of positive solutions to a Neumann problem involving the p-Laplacian are established. Multiplicity results are also pointed out.  ...  ensures two positive weak solutions while Theorem 4.3 ensures three positive weak solutions (see proof of Theorem 3.3).  ...  u ( 0 )= 0 . 00 u + a(x)|u| p−2 u = λ u 2p + 1 in Ω, ∂u ∂ν = 0 o n ∂Ω,admits at least two positive weak solutions.  ...

### Semi-simplicity of a proper weakH*-algebra

Parfeny P. Saworotnow
1992 International Journal of Mathematics and Mathematical Sciences
It is shown that a proper (eachxris unique) weak rightH*-algebra is semi-simple. Also there is an example of weak rightH*-algebra which is not a leftH*-algebra.  ...  A weak rightH*-algebra is a Banach algebraAwhich is a Hilbert space and which has a dense subsetDrwith the property that for eachxinDrthere existsxrsuch that(yx,z)=(y,zxr)for ally,zinA.  ...  However, there is a different story for the case of a two-sided (weak) H*-algebra.  ...

### A New Asymptotic Notation: Weak Theta

Andrei-Horia Mogoş, Bianca Mogoş, Adina Magda Florea
2015 Mathematical Problems in Engineering
In addition, in order to highlight the main particularities of Weak Theta, we propose and prove several theoretical results: properties of Weak Theta, criteria for comparing two complexity functions, and  ...  In this paper, we define a new asymptotic notation, called "Weak Theta," that uses the comparison of various complexity functions with two given complexity functions.  ...  ; (iv) properties related to "Weak Theta" and the set of complexity functions comparable with two given complexity functions.  ...

### Parity Violation in Weak Nuclear Interactions

Brian Albert Robson
2022 Journal of High Energy Physics Gravitation and Cosmology
: in the GM, the observed parity violations arise as a consequence of the negative intrinsic parity of both the W massive bosons, which mediate these so-called charge-changing (CC) weak nuclear interactions  ...  The treatment of parity violations in the weak nuclear interactions is discussed within the frameworks of both the Standard Model (SM) and the Generation Model (GM) of particle physics.  ...  Third, the treatment of the universality of the weak nuclear force differs considerably within the two models.  ...

### Derivations onB∗algebras

Philip Miles
1964 Pacific Journal of Mathematics
That S is in the weak closure of φ{A) is a consequence of the fact [3, Cor. 4 ] that our choice of ^ causes the weak closure of φ(A) to be the C* direct sum Σ 0 (H f ) extended over ^Γ We have been operating  ...  As a sample consequence, we give two generalizations of Wielandt's result that if K is a self-ad joint element of & (H), there is no -X" in & (H) such that KX -XK = il; we view this as saying that Ό κ  ...

### Representation of Uncertainty for Limit Processes [article]

Mark Burgin
2001 arXiv   pre-print
To take into account the intrinsic uncertainty of a model, it is suggested to use fuzzy derivatives instead of conventional derivatives of functions in this model.  ...  In the paper, a mathematical approach to such kind of uncertainty, which emerges in computation and measurement, is suggested on the base of the concept of a fuzzy limit.  ...  weak 0-derivative w of f at x for which ρ(b, w)= d.  ...

### Strong versus weak quantum consequence operations

Jacek Malinowski
1992 Studia Logica: An International Journal for Symbolic Logic
This paper is a study of similarities and di erences between strong and weak quantum consequence operations determined by a given class of ortholattices.  ...  In the papers concerning quantum logics, there exist two di erent notions of logical consequences determined by a class of ortholattices.  ...  Let In the next part of the paper we will work only with the sentential language S = S; _;^; 0 with two binary connectives _ and^and the unary one 0 .  ...

### Strong diameter two property and convex combination of slices reaching the unit sphere [article]

Gines Lopez-Perez, Miguel Martin, Abraham Rueda Zoca
2019 arXiv   pre-print
slices of the unit ball contains two points at distance exactly two.  ...  We characterise the class of those Banach spaces in which every convex combination of slices of the unit ball intersects the unit sphere as the class of those spaces in which every convex combination of  ...  In the case that X is a dual space, we say that X has the weak * -strong diameter two property (weak * -SD2P in short) if every convex combination of weak-star slices of B X has diameter two.  ...

### THE ANTISYMMETRIZED WEAK COUPLING SCHEME IN SHELL MODEL CALCULATIONS

S. K. M. WONG, A. P. ZUKER
1971 Le Journal de Physique Colloques
-Shell model calculations are carried out in an antisymmetrized weak coupling basis.  ...  Dramatic reductions in dimensionality and great gains of physical insight are achieved, when compared with conventional results.  ...  In any case there is not much to choose between the two schemes and the consequences of this equivalence may be quite interesting.  ...

### The Scott topology of a rooted non-metric tree [article]

Josnei Novacoski
2015 arXiv   pre-print
Moreover, for each t∈ T, we consider a natural order ≼_t on T under which t is the root of T. Then the weak tree topology is generated by the union of the Scott topologies S_t associated to ≼_t.  ...  In this paper we prove that the Scott topology S on a rooted non-metric tree T is strictly coarser than the weak tree topology.  ...  Consequently, the weak tree topology on T defined by these two orders is the same. The following lemma will be used in the proof of the main theorem.  ...
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