Object of the present paper is to study pseudo Hermitian magnetic curves in (κ,µ) manifold admitting Zamkovoy connection. We give main classification theorem for pseudo-Hermitian curve. Again we find curvature and torsion a (κ,µ)-manifold

κ-carbide hardening in a ferrite-austenite duplex low-density FeMnAlC steel has been investigated as a function of annealing processing within the temperature range 500−900 o C. Below 600 o C, a high hardness can be attained by the fine microstructures, e.g. the thin lamellar κ-carbides in austenite and dispersed nanosized particulate κ-carbides in ferrite. After further annealing, the alloy so...

We explore two possible generalizations of the Euler formula for the complex κ-exponential, which give two different sets of κ-deformed cyclic functions endowed with different analytical properties. In a case, the κ-sine and κ-cosine functions take real values on R and are characterized by an asymptotic log-periodic behavior. In the other case, the κ-cyclic functions take real values only in th...

Our aim is to show the consistency of 2κ ≥ κ+θ, for any θ < κ starting with a singular cardinal κ of cofinality ω so that ∀n < ω∃α < κ(o(α) = α). Dropping cofinalities technics are used for this purpose. 1 א1-gap and infinite drops in cofinalities Let κ be a singular cardinal of cofinality ω such that for each γ < κ and n < ω there is α, γ < α < κ, such that o(α) = α. We fix a sequence of cardi...

The continuum function F on regular cardinals is known to have great freedom; if α, β are regular cardinals, then F needs only obey the following two restrictions: (1) cf(F (α)) > α, (2) α < β → F (α) ≤ F (β). However, if we wish to preserve measurable cardinals in the generic extension, new restrictions must be put on F . We say that κ is F (κ)-hypermeasurable if there is an elementary embeddi...

We improve the geometric properties of SLE(κ; ~ ρ) processes derived in an earlier paper, which are then used to obtain more results about the duality of SLE. We find that for κ ∈ (4, 8), the boundary of a standard chordal SLE(κ) hull stopped on swallowing a fixed x ∈ R \ {0} is the image of some SLE(16/κ; ~ ρ) trace started from a random point. Using this fact together with a similar propositi...

narrowing ABSTRACT NARROWING u∈ Onv (g) & (l=r ⇐ C) << R A & κ = mgu ({g|u,l}) ––––––––––––––––––––––––––––––––––––––– g ⇒κ (C, g[r]u)κ  abstract semantics of a goal g ∆(g)= {κ| g ⇒κ* true} (decidable)  the abstract semantics approximates the concrete semantics ∀ σ ∈ O(g). ∃ κ ∈ ∆(g). κ ≤ σ  unsatisfiability analysis ∆(g)=∅ ⇒ g es unsatisfiable  abstract basic narrowing is compositional ∆(g...

We generalize ∇(A), which was introduced in [Sch∞], to larger cardinals. For a regular cardinal κ > א0 we denote by ∇κ(A) the statement that A ⊆ κ and for all regular θ > κ, {X ∈ [Lθ[A] ] <κ : X ∩ κ ∈ κ ∧ otp(X ∩ Ord) ∈ Card} is stationary in [Lθ[A] ] . It was shown in [Sch∞] that ∇א1(A) can hold in a set-generic extension of L. We here prove that ∇א2(A) can hold in a set-generic extension of L...

Strengthening a result of Amir Leshem [7], we prove that the consistency strength of holding GCH together with definable tree property for all successors of regular cardinals is precisely equal to the consistency strength of existence of proper class many Π 1 reflecting cardinals. Moreover it is proved that if κ is a supercompact cardinal and λ > κ is measurable, then there is a generic extensi...

A question of Woodin asks if κ is strongly compact and GCH holds below κ, then must GCH hold everywhere? One variant of this question asks if κ is strongly compact and GCH fails at every regular cardinal δ < κ, then must GCH fail at some regular cardinal δ ≥ κ? Another variant asks if it is possible for GCH to fail at every limit cardinal less than or equal to a strongly compact cardinal κ. We ...