New Pool Boiling Heat Transfer in the Presence of Low-Frequency Vibrations Into a Vertical Cylindrical Heat Source

A vertical cylinder was applied as a heat source into a water pool; the vibrations were imposed into the heater with different heat fluxes, and the frequencies were adjusted at 10, 15, 20, and 25 Hz. An imaging system was employed to observe the produced bubbles around the cylindrical heat source. The results showed that the boiling heat transfer was enhanced under the vibrations with a shorter transient process, and the wall temperature also decreased. The best enhancement ratio was achieved at the frequency of 25 Hz and a heat flux value of 30 kW/m² as a consequence of imposed vibrations.     

Localized vibrational mode in manganese-doped zinc oxide

The diluted magnetic semiconductor, ZnO:Mn, is studied here theoretically for the defect modes, as this is not well documented in the literature, even though other investigations are reported. Theoretical results are compared with the experimental results.     

Efficient solutions in generalized linear vector optimization

This paper establishes several new facts on generalized polyhedral convex sets and shows how they can be used in vector optimization. Among other things, a scalarization formula for the efficient solution sets of generalized linear vector optimization problems is obtained. We also prove that the efficient solution set of a generalized linear vector optimization problem in a locally convex Hausdorff topological vector space is the union of finitely many generalized polyhedral convex sets and it is connected by line segments.     

On spectral resolutions connected with self-adjoint differential vector-operators in a Hilbert space

We show that spectral resolutions of differential vector-operators may be represented as a specific direct sum integral operator with a kernel written in terms of generalized vector-operator eigenfunctions. Then we prove that a generalized eigenfunction measurable with respect to the spectral parameter may be decomposed using a set of analytical defining systems of coordinate operators.     

A note on reverse derivations

In this note, the notion of reverse derivation is studied. It is shown that in the class of semiprime rings, this notion coincides with the usual derivation when it maps a semiprime ring into its centre. However, we provide some examples to show that it is not the case in general.     

On sub‐Riemannian geodesics on the Engel groups: Hamilton's equations

We study the sub‐Riemannian geometry on the Engel group which is a step 3 nilpotent Lie group on . Our main result is to solve the Hamiltonian equations associated with the bi‐characteristic curves and express the solutions in terms of elliptic functions. Our model covers both the Heisenberg group and the Martinet case when setting certain parameters to be zero.     

Globally generated vector bundles on with

One classifies the globally generated vector bundles on with the first Chern class c₁ = 3. The case c₁ = 1 is very easy, the case c₁ = 2 was done in [42], the case c₁ = 3, rank =2 was settled in [21] and the case c₁ ≤ 5, rank = 2 in [10]. Our work is based on Serre's theorem relating vector bundles of rank = 2 with codimension 2 lci subschemes and its generalization for higher ranks, considered firstly by Vogelaar in [48].     

Hom-Orthogonal Partial Tilting Modules for Dynkin Quivers

We count the number of isomorphism classes of hom-orthogonal partial tilting modules over path algebras of Dynkin quiver of type 𝔸 _n , 𝔻 _n , 𝔼 _n . This number is independent on the choice of an orientation of the arrows, and the number for 𝔸 _n or 𝔻 _n -type can be expressed as a special value of a hypergeometric function. As a consequence of our theorem, we obtain a minimum value of the number of basic relative invariants of corresponding regular prehomogeneous vector spaces.     

Root Systems In Finite Symplectic Vector Spaces

We study realizations of root systems in possibly degenerate symplectic vector spaces over finite fields, up to symplectic isomorphisms. The main result of this article is the classification of such realizations for the field 𝔽₂. Thereby, each root system requires a specific degree of degeneracy of the symplectic vector space. Our main motivation for this article is that for each such realization of a root system we can construct a Nichols algebra over a nonabelian group.     

参数弱向量平衡问题解集的似Holder性和相依导数

本文研究了一类参数弱向量平衡问题解集的似Hölder性和相依导数. 首先, 讨论了该问题的一类实值间隙函数的Lipschitz连续性和Hadamard方向可微性. 然后, 借助这些性质, 建立了该问题解集的似Hölder性和Hölder连续性以及相依导数的具体表达式.