A first-order differential double subordination with applications

Let $q_1$ and $q_2$ belong to a certain class of normalized analytic univalent functions in the open unit disk of the complex plane. Sufficient conditions are obtained for normalized analytic functions $p$ to satisfy the double subordination chain $q_1(z)\prec p(z)\prec q_2(z)$. The differential sandwich-type result obtained is applied to normalized univalent functions and to $\Phi$-like functions

Cluster description of cold (neutronless) alpha ternary fission of 252Cf

A coplanar three body cluster model (two deformed fragments and an alpha particle) similar to the model used for the description of cold binary fission was employed for the description of cold (neutronless) alpha accompanied fission of 252Cf. No preformation factors were considered. The three body potential was computed with the help of a double folding potential generated by the M3Y-NN effective interaction and realistic fragment ground state deformations. From the minimum action principle, the alpha particle trajectory equations, the corresponding ternary barriers, and an approximate WKB expression for the barrier penetrability are obtained. The relative cold ternary yields were calculated as the ratio of the penetrability of a given ternary fragmentation and the sum of the penetrabilities of all possible cold ternary fragmentations. Different scenarios were considered depending on the trajectories of the fragments. It was shown that two regions of cold fragmentation exist, a deformed one corresponding to large fragment deformations and a spherical one around 132Sn, similarly to the case of the cold binary fission of 252Cf. We have shown that for the scenario corresponding to the Lagrange point, where all forces acting on the alpha particle are in equilibrium, the cold alpha ternary yields of 252Cf are strongly correlated with the cold binary yields of the daughter nucleus 248Cm into the same heavy fragments. For all other scenarios only the spherical splittings are favored. We concluded that due to the present available experimental data on cold alpha ternary yields only the Lagrange scenario could describe the cold alpha ternary fission of 252Cf

Certain sufficient conditions for close-to-convexity and starlikeness of multivalent functions

By using Jack's lemma, we derive simple sufficient conditions for analytic functions to be multivalent close-to-convex and multivalent starlike

ChatGPT Performances in Explanation of Physiopathology by Example

Physiopathology constitutes one of the basic disciplines that helps understand the mechanisms of diseases and, consequently, access effective and personalized therapies. ChatGPT is a working tool that promptly provides detailed answers to targeted questions, revolutionizing the way medical professionals interact with artificial intelligence (AI). The purpose of this study was to compare the answers provided by human intelligence with experience and professional qualification with the answers provided by ChatGPT, regarding the targeted questions addressed to one clinical case, to decipher the key pathophysiological mechanisms. The input was represented by cases published in Bulboacă et al.1 ChatGPT-3.5 (https://chat.openai.com/) free version was used in our study. We provide one case (in Romanian language) and ask ChatGPT to answer five individual questions. We collected the answers on August 7, 2023. The following request was included in the ChatGPT window: We have the following case: “[case description]”. Answer the following questions: [questions]. The evaluation of the responses given by the ChatGPT was done by one researcher and classified as correct, partially correct, or incorrect. The AI generated answers were partially correct in 4 out of 5 questions and incorrect in one question. ChatGPT can be a valuable instrument for medical teaching, but answer analyses must be added to ensure the validity of the responses and explanations

A class of superordination-preserving convex integral operator

If $H(mathrm{U})$ denotes the space of analytic functions in the unit disk $mathrm{U}$, for the integral operator $A_{alpha,beta,gamma,delta}^h:mathcal Krightarrow H(mathrm{U})$, with $mathcal Ksubset H(mathrm{U})$, defined by [ A_{alpha,beta,gamma,delta}^h[f](z)=left[frac{beta+gamma}{z^gamma} int_0^zf^alpha(t)h(t)t^{delta-1}operatorname{d}tright]^{1/beta},; Big(alpha,beta,gamma,deltainmathbb{C};text{and};;hin H(mathrm{U})Big), ] we will determine sufficient conditions on $g_1$, $g_2$, $alpha$, $beta$ and $gamma$ such that [ zh(z)left[frac{g_1(z)}{z}right]^alphaprec zh(z)left[frac{f(z)}{z}right]^alphaprec zh(z)left[frac{g_2(z)}{z}right]^alpha ] implies [ zleft[frac{A_{alpha,beta,gamma,delta}^h[g_1](z)}{z}right]^betaprec zleft[frac{A_{alpha,beta,gamma,delta}^h[f](z)}{z}right]^betaprec zleft[frac{A_{alpha,beta,gamma,delta}^h[g_2](z)}{z}right]^beta. ] In addition, both of the subordinations are sharp, since the left-hand side will be the largest function, and the right-hand side will be the smallest function so that the above implication has been held for all $f$ functions satisfying the double differential subordination of the assumption. The results generalize those of the last author from cite{bul3}, obtained for the special case $alpha=beta$ and $hequiv1$

Importance of specific rehabilitation methods for patients with intracerebral hemorrage

Intracerebral hemorrhage (ICH) is a severe type of stroke which causes bleeding in the brain parenchyma, accounting for 10-15% of all strokes. Prognosis of patients with ICH remains very poor despite new advances in management strategies, and has not improved in the last decades. Disability remains important in ICH survivors, only a small proportion of patients live an independent life after ICH. Development of new strategies in rehabilitation care is expected to improve survival and outcome after intracerebral hemorrhage. The main neurological sequellae after ICH are similar to those seen after ischemic stroke. Given the clinical and pathological differences between the two types of stroke, clinical recovery is expected to be different. Comparisons between rehabilitation results in hemorrhagic versus ischemic stroke have offered mixed results, but all of them agreed that rehabilitation is highly effective after hemorrhagic strokes. There are no standard recommendations regarding the specific procedures used in the rehabilitation program of ICH patients. In the absence of clinical data to guide specific practice, the rehabilitation of ICH patients is largely based on general principles learned from ischemic stroke recovery. Physical therapy, task-specific training, sensory stimulation, use of assistive devices for upper limb or gait functions, speech and language therapy, physiotherapy and balnear therapy are methods used in rehabilitation of patients with hemorrhagic stroke, with improvement in patients functional outcome. There is a need for further development of specific rehabilitation techniques to enhance recovery in ICH patients