On the rescaled Riemannian metric of Cheeger Gromoll type on the cotangent bundle

Let $(M,g)$ be an n-dimensional Riemannian manifold and $T^{*}M$ be its cotangent bundle equipped with a Riemannian metric of Cheeger Gromoll type which rescale the horizontal part by a nonzero differentiable function. The main purpose of the present paper is to discuss curvature properties of $T^{*}M$ and construct almost paracomplex Norden structures on $T^{*}M$. We investigate conditions for these structures to be para-K\"ahler (paraholomorphic) and quasi-K\"ahler. Also, some properties of almost paracomplex Norden structures in context of almost product Riemannian manifolds are presented

Finite state verifiers with both private and public coins

We consider the effects of allowing a finite state verifier in an interactive proof system to use a bounded number of private coins, in addition to "public" coins whose outcomes are visible to the prover. Although swapping between private and public-coin machines does not change the class of verifiable languages when the verifiers are given reasonably large time and space bounds, this distinction has well known effects for the capabilities of constant space verifiers. We show that a constant private-coin "budget" (independent of the length of the input) increases the power of public-coin interactive proofs with finite state verifiers considerably, and provide a new characterization of the complexity class $\rm P$ as the set of languages that are verifiable by such machines with arbitrarily small error in expected polynomial time.Comment: 18 pages, of which 5 pages are appendix, accepted for presentation in the conference ICTCS 2023, and is to be published in its proceeding

Primary psoas muscle abscess diagnosed and treated during pregnancy: case report and literature review.

BACKGROUND: Primary psoas muscle abscess is rare and can be difficult to diagnose, particularly during pregnancy. CASE: To our knowledge, this is the first case of primary psoas muscle abscess diagnosed during pregnancy. Clinical investigation did not reveal any infection spreading from adjacent structures. Surgical drainage and simultaneous Cesarean delivery of the infant, combined with appropriate antibiotics, enabled a cure. CONCLUSION: The possibility of psoas muscle abscess should be taken into account when investigating lower back pain during pregnancy if conventional approaches are unsatisfactory

Properties of Modified Riemannian Extensions

Let M be an n-dimensional differentiable manifold with a symmetric connection ∇ and T*M be its cotangent bundle. In this paper, we study some properties of the modified Riemannian extension ğ∇, c on T*M defined by means of a symmetric (0, 2)-tensor field c on M. We get the conditions under which T*M endowed with the horizontal lift HJ of an almost complex structure J and with the metric ğ∇, c is a Kähler-Norden manifold. Also curvature properties of the Levi-Civita connection of the metric ğ∇, c are presented.Пусть M - n-мерное дифференцируемое многообразие с симметричной связностью ∇ а T*M - его кокасательное расслоение. В статье изучены некоторые свойства модифицированного риманова расширения ğ ∇, c на T*M, которое определяется с помощью симметричного (0, 2)-тензорного поля c на M. Получены условия, при которых T*M, наделенное горизонтальным лифтом HJ почти комплексной структуры J и метрикой ğ∇, c, является многообразием Kэлера-Нордена. Также представлены свойства кривизны связности Леви- Чивита метрики ğ ∇ , c.Нехай M — n-мірний диференційовний многовид із симетричного зв'язністго ∇, а T*M — його кодотичне розшарування. В статті вивчено деякі властивості модифікованого ріманова розширення ğ ∇, c на T*M, яке визначається за допомогою симетричного (0, 2)-тензорного поля с на М. Отримано умови, за яких T*M, наділене горизонтальним ліфтом HJ майже комплексної структури J і метрикого ğ∇, c, є многовидом Келера-Нордена. Також представлені властивості кривини зв'язності Леві-Чівіти метрики ğ∇, c

Some Properties Concerning Curvature Tensors of Eight-Dimensional Walker Manifolds

The main purpose of the present paper is to study conditions for the eight-dimensional Walker manifolds which admit a field of parallel null 4-planes to be Einsteinian, Osserman, or locally conformally flat.Основной целью данной статьи является изучение условий, при которых восьмимерные многообразия Уолкера, допускающие поле параллельных нулевых четырехмерных плоскостей, являются эйнштейновыми, оссермановыми или локально конформно плоскими

Antioxidant and antimicrobial activities of Morchella conica Pers.

Antioxidant capacity and antimicrobial activities of Morchella conica Pers. extracts obtained with ethanol were investigated in this study. Four complementary test systems; namely DPPH free radical scavenging, -carotene/linoleic acid systems, total phenolic compounds and total flavonoid concentration were used. Inhibition values of M. conica ethanol extracts, buthylated hydroxyanisol (BHA) and -tocopherol standards were found to be 96.9, 98.9 and 99.2%, respectively, at aconcentration of 160 ìg/ml. When compared the inhibition levels of methanol extract of M. conica and standards in linoleic acid system, it was observed that the higher the concentration of both M. conicaethanol extract and the standards the higher the inhibition effect. Total flavonoid amount was 9.17±0.56ìg mg-1 quercetin equivalent while the phenolic compound amount was 41.93±0.29 ìg mg-1 pyrocatecholequivalent in the ethanolic extract. The antimicrobial effect of M. conica ethanol extract was tested against six species of Gram-positive bacteria, seven species of Gram-negative bacteria and one speciesof yeast. The M. conica ethanol extract had a narrow antibacterial spectrum against tested microorganisms. The most susceptible bacterium was M. flavus. The crude extract was found active on S. aureus ATCC 25923 and S. aureus Cowan I. The M. conica ethanol extract did not exhibit anticandidal activity against C. albican