Riemann Hypothesis Holds virtually true

If infinity times zero equal zero then Zeta function has an analytic continuity over the whole complex plan except a simple pole at 1. Since infinity times zero is undefined, then Riemann' s approach remain not sharp. However, it is true that the non trivial zeros lie at the critical line x = 1/2 despite there simultaneous virtual existence or in another words, such zeros are assumed to exist.

Note on composition of entire functions and bounded $L$-index in direction

We study the following question: ``Let $f\colon \mathbb{C}\to \mathbb{C}$ be an entire function of bounded $l$-index, $\Phi\colon \mathbb{C}^n\to \mathbb{C}$ an be entire function, $n\geq2,$ $l\colon \mathbb{C}\to \mathbb{R}_+$ be a continuous function. What is a positive continuous function $L\colon \mathbb{C}^n\to \mathbb{R}_+$ and a direction $\mathbf{b}\in\mathbb{C}^n\setminus\{\mathbf{0}\}$ such that the composite function $f(\Phi(z))$ has bounded $L$-index in the direction~$\mathbf{b}$?'' In the present paper, early known result on boundedness of $L$-index in direction for the composition of entire functions $f(\Phi(z))$ is modified. We replace a condition that a directional derivative of the inner function $\Phi$ in a direction $\mathbf{b}$ does not equal zero. The condition is replaced by a construction of greater function $L(z)$ for which $f(\Phi(z))$ has bounded $L$-index in a direction. We relax the condition $|\partial_{\mathbf{b}}^k\Phi(z)|\le K|\partial_{\mathbf{b}}\Phi(z)|^k$ for all $z\in\mathbb{C}^n$,where $K\geq 1$ is a constant and ${\partial_{\mathbf{b}} F(z)}:=\sum\limits_{j=1}^{n}\!\frac{\partial F(z)}{\partial z_{j}}{b_{j}}, $ $\partial_{\mathbf{b}}^k F(z):=\partial_{\mathbf{b}}\big(\partial_{\mathbf{b}}^{k-1} F(z)\big).$ It is replaced by the condition $|\partial_{\mathbf{b}}^k\Phi(z)|\le K(l(\Phi(z)))^{1/(N(f,l)+1)}|\partial_{\mathbf{b}}\Phi(z)|^k,$ where $N(f,l)$ is the $l$-index of the function $f.$The described result is an improvement of previous one.

COVID-19: Do DNA / RNA vaccines integrate into the genome?

The new coronavirus pandemic brought the need for researchers to work tirelessly in the search for therapies or vaccines that would allow control of the spread of the virus around the world. Fortunately there are two RNA vaccines against COVID-19 that have finished clinical tests and are approved in some countries. They are the first third generation vaccines approved in history and in time record. But still have some concerns about safety of DNA/RNA vaccines. Here we bring a discussion about safety of DNA/RNA: can these vaccines be integrated to the genome? In fact, DNA vaccines have an infinite chance to integrate in the cell's genome, but this infinite chance is equal zero when used with RNA-based vaccines. The vaccines based on nucleic acid (DNA and RNA) have been corresponding in advantages, becoming promising alternatives to guarantee the immunization of the new coronavirus.

Some Remarks and Propositions on Riemann Hypothesis

In this article we look at some well know results of Riemann Zeta function in a different light. We explore the proofs of Zeta integral Representation, Analytic continuity and the first functional equation. We propound some modifications in order to reasonably justify the location of the non-trivial zeros on the critical line: s= 1/2 by assuming that ζ(s) and ζ(1-s) simultaneously equal zero

Biquaternionic Dirac Equation Predicts Zero Mass for Majorana Fermions

A biquaternionic version of the Dirac Equation is introduced, with a procedure for converting four-component spinors to elements of the Pauli algebra. In this version, mass appears as a coefficient between the 4-gradient of a spinor and its image under an outer automorphism of the Pauli algebra. The charge conjugation operator takes a particulary simple form in this formulation and switches the sign of the mass coefficient, so that for a solution invariant under charge conjugation the mass has to equal zero. The multiple of the charge conjugation operator by the imaginary unit turns out to be a complex Lorentz transformation. It commutes with the outer automorphism, while the charge conjugation operator itself anticommutes with it, providing a second more algebraic proof of the main theorem. Considering the Majorana equation, it is shown that non-zero mass of its solution is imaginary.

VEITSMAN’S THEOREM ON SPACES AND FORCES FORMING THEM, TIME AND CHAOS

Some consequences follow from Veitsman’s theorem. It is supposed that our physical time is a criterion characterizing the flow of any fundamental process. It is supposed as well that physical time in space defines from the state of the system under study, e.g., of Universe. If the space is in equilibrium then there is no time known to us from physics in it. The physical time appears in case when the energy expenses take place during the process flowing in space studied. If the space is anisotropic then the time is to be a tensor of rank 2 when its off-diagonal components equal zero. The anisotropy of the space and the change of the physical time passage lead to the breach of the causal connections in the system under study and, as a result, to chaos in it.

AN OVERVIEW OF THE OPTIONS WITHIN AN ISLAMIC CONTEXT

The investors search the financial instruments which contain least cost and reduced risk. As a recap, the financial instrument is negotiable contracts and they are two sorts, at the: • First, the traditional assets financials with that are negotiated in market of the stock exchange (shares, bonds, and the part in organism for collective investment in securities value …) or other cash instruments such as loans and deposits commercialize in the market; • Second, the derived financial product: there are two types of contracts, for the one a close position like (forwards, futures, swaps) and for the other one, the optional position likes options or warrants. So, all Islamic country observes that the option hasn’t legitimate in stock exchange and it has for originate most of the doctrine of Islam prohibit the transaction with all kinds of options,this implies a complete absence of options in the financial markets of Muslim countries and this context a random yield with in the money (ITM) of option equal zero.

Petersen’s Space Internal Hernia after Laparoscopic One Anastomosis (Mini) Gastric Bypass

Background. One anastomosis gastric bypass (OAGB) is now considered as an appropriate alternative for Roux-en-Y gastric bypass (RYGB) with some advantages such as absence of risk for internal hernia (IH). But, is really the risk of IH equal zero after OAGB? Case Summary. A 37-year-old male was admitted due to severe abdominal crampy pain, nausea, vomiting, and obstipation. He had chronic and intermittent abdominal pain from 2 years after OAGB. With high suspicion of complete obstruction, the exploratory laparoscopy was performed. Intraoperative findings showed incarcerated bowel hernia from Petersen’s defect. The incarcerated bowel was reduced, and the defect was repaired. The patient was discharged 2 days after operation. Conclusion. The incidence of IH after OAGB is rare but not zero. In any suspicious signs and symptoms for IH, the early exploratory laparoscopy is mandatory to diagnose and treat.