Given an ideal I on ω let a(I) (ā(I)) be minimum of the cardinalities of in nite (uncountable) maximal I-almost disjoint subsets of [ω]. We show that a(Ih) > ω if Ih is a summable ideal; but a(Z~ μ) = ω for any tall density ideal Z~ μ including the density zero ideal Z. On the other hand, you have b ≤ ā(I) for any analytic P -ideal I, and ā(Z~ μ) ≤ a for each density ideal Z~ μ. For each ideal ...

We consider complete first-order theories T with infinite models. Additionally we assume that T are small, i. e., they have countably many types (|S(T )| = ω). So for any type q ∈ S(T ) and its realization ā, there exists a model M(ā), being prime over ā. Since all prime models over realizations of q are isomorphic, we often denote such by Mq. Let p and q be types in S(T ). We say that the type...

The innermost stable circular orbits (ISCO) of coalescing neutron starblack hole binary are studied taking into account both the tidal and relativistic effects. We adopt the generalized pseudo-Newtonian potential to mimic the general relativistic effects of gravitation. It is found that the separation of the neutron star and the black hole at the innermost stable circular orbit is greater than ...

Let m and n be positive integers, and let R = (r1, . . . , rm) and S = (s1, . . . , sn) be non-negative integral vectors. Let A(R, S) be the set of all m× n (0, 1)-matrices with row sum vector R and column vector S, and let Ā be the m × n (0, 1)-matrix where for each i, 1 ≤ i ≤ m, row i consists of ri 1’s followed by n − ri 0’s. If S is monotone, the discrepancy d(A) of A is the number of posit...

A linear order is n-decidable if its universe is N and the relations determined by n formulas are uniformly computable. This means that there is a computable procedure which, when applied to a n formula φ(x̄) and a sequence ā of elements of the linear order, will determine whether or not φ(ā) is true in the structure. A linear order is decidable if the relations determined by all formulas are un...

Let A = Fq [T ] be the ring of polynomials over the finite field Fq and 0 = a ∈ A. Let C be the A-Carlitz module. For a monic polynomial m ∈ A, let C(A/mA) and ā be the reductions of C and a modulo mA respectively. Let fa(m) be the monic generator of the ideal {f ∈ A,Cf (ā) = 0̄} on C(A/mA). We denote by ω(fa(m)) the number of distinct monic irreducible factors of fa(m). If q = 2 or q = 2 and a ...

We correct the results in Section V of the above mentioned manuscript. In [1], we showed that a particular class of networked control system (NCS) with quantization, i.i.d. dropouts and disturbances can be described as a Markov jump linear system of the form θk+1 = Ā(dk)θk + B̄(dk)νk, (1)

We investigate a notion called uniqueness in power κ that is akin to categoricity in power κ, but is based on the cardinality of the generating sets of models instead of on the cardinality of their universes. The notion is quite useful for formulating categoricity-like questions regarding powers below the cardinality of a theory. We prove, for (uncountable) universal theories T , that if T is κ...

couplings are needed to explain the RD and RD∗ anomalies. We show that when the upper limit of BR(Bc → τ ν̄τ ) < 30% is included, RD can be significantly enhanced while RD∗ < 0.27. With the BR(Bc → τ ν̄τ ) constraint, we find that the τ -lepton polarizations can be still affected by the charged-Higgs effects, where the standard model (SM) predictions are obtained as: P τ D ≈ 0.324 and P τ D∗ ≈ −0...