scholarly journals Disproof of the Riemann Hypothesis

2021 ◽  
Author(s):  
Frank Vega
Keyword(s):  
Positive Constant ◽  
Riemann Hypothesis ◽  
A Value ◽  
Large Numbers

We define the function $\upsilon(x) = \frac{3 \times \log x + 5}{8 \times \pi \times \sqrt{x} + 1.2 \times \log x + 2} + \frac{\log x}{\log (x + C \times \sqrt{x} \times \log \log \log x)} - 1$ for some positive constant $C$ independent of $x$. We prove that the Riemann hypothesis is false when there exists some number $y \geq 13.1$ such that for all $x \geq y$ the inequality $\upsilon(x) \leq 0$ is always satisfied. We know that the function $\upsilon(x)$ is monotonically decreasing for all sufficiently large numbers $x \geq 13.1$. Hence, it is enough to find a value of $y \geq 13.1$ such that $\upsilon(y) \leq 0$ since for all $x \geq y$ we would have that $\upsilon(x) \leq \upsilon(y) \leq 0$. Using the tool $\textit{gp}$ from the project PARI/GP, we found the first zero $y$ of the function $\upsilon(y)$ in $y \approx 8.2639316883312400623766461031726662911 \ E5565708$ for $C \geq 1$. In this way, we claim that the Riemann hypothesis could be false.

scholarly journals Disproof of the Riemann Hypothesis

2021 ◽  
Author(s):  
Frank Vega
Keyword(s):  
Positive Constant ◽  
Riemann Hypothesis ◽  
A Value ◽  
Large Numbers

We define the function $\upsilon(x)=\frac{3 \times \log x+5}{8 \times \pi \times \sqrt{x}+1.2 \times \log x+2}+\frac{\log x}{\log (x + C \times \sqrt{x} \times \log \log \log x)} - 1$ for some positive constant $C$ independent of $x$. We prove that the Riemann hypothesis is false when there exists some number $y \geq 13.1$ such that for all $x \geq y$ the inequality $\upsilon(x) \leq 0$ is always satisfied. We know that the function $\upsilon(x)$ is monotonically decreasing for all sufficiently large numbers $x \geq 13.1$. Hence, it is enough to find a value of $y \geq 13.1$ such that $\upsilon(y) \leq 0$ since for all $x \geq y$ we would have that $\upsilon(x) \leq \upsilon(y) \leq 0$. Using the tool $\textit{gp}$ from the project PARI/GP, we note that $\upsilon(100!) \approx \textit{-2.938735877055718770 E-39} < 0$ for all $C \geq \frac{1}{1000000!}$. In this way, we claim that the Riemann hypothesis could be false.

scholarly journals Disproof of the Riemann Hypothesis

2021 ◽  
Author(s):  
Frank Vega
Keyword(s):  
Positive Constant ◽  
Riemann Hypothesis ◽  
A Value ◽  
Large Numbers

We define the function $\upsilon(x)=\frac{3 \times \log x+5}{8 \times \pi \times \sqrt{x}+1.2 \times \log x+2}+\frac{\log x}{\log (x + C \times \sqrt{x} \times \log \log \log x)} - 1$ for some positive constant $C$ independent of $x$. We prove that the Riemann hypothesis is false when there exists some number $y \geq 13.1$ such that for all $x \geq y$ the inequality $\upsilon(x) \leq 0$ is always satisfied. We know that the function $\upsilon(x)$ is monotonically decreasing for all sufficiently large numbers $x \geq 13.1$. Hence, it is enough to find a value of $y \geq 13.1$ such that $\upsilon(y) \leq 0$ since for all $x \geq y$ we would have that $\upsilon(x) \leq \upsilon(y) \leq 0$. Using the tool $\textit{gp}$ from the project PARI/GP, we note that $\upsilon(100!) \approx \textit{-2.938735877055718770 E-39} < 0$ for all $C \geq \frac{1}{1000000!}$. In this way, we claim that the Riemann hypothesis could be false.

scholarly journals Disproof of the Riemann Hypothesis

2021 ◽  
Author(s):  
Frank Vega
Keyword(s):  
Positive Constant ◽  
Riemann Hypothesis ◽  
A Value ◽  
Large Numbers

We define the function $\upsilon(x) = \frac{3 \times \log x + 5}{8 \times \pi \times \sqrt{x} + 1.2 \times \log x + 2} + \frac{\log x}{\log (x + C \times \sqrt{x} \times \log \log \log x)} - 1$ for some positive constant $C$ independent of $x$. We prove that the Riemann hypothesis is false when there exists some number $y \geq 13.1$ such that for all $x \geq y$ the inequality $\upsilon(x) \leq 0$ is always satisfied. We know that the function $\upsilon(x)$ is monotonically decreasing for all sufficiently large numbers $x \geq 13.1$. Hence, it is enough to find a value of $y \geq 13.1$ such that $\upsilon(y) \leq 0$ since for all $x \geq y$ we would have that $\upsilon(x) \leq \upsilon(y) \leq 0$. Using the tool $\textit{gp}$ from the project PARI/GP, we note that $\upsilon(100!) \approx \textit{-2.938735877055718770 E-39} &lt; 0$ for all $C \geq \frac{1}{1000000!}$. In this way, we claim that the Riemann hypothesis could be false.

scholarly journals Another Criterion For The Riemann Hypothesis

2021 ◽  
Author(s):  
Frank Vega
Keyword(s):  
Positive Constant ◽  
Riemann Hypothesis ◽  
Chebyshev Function

Let's define $\delta(x)=(\sum_{{q\leq x}}{\frac{1}{q}}-\log \log x-B)$, where $B \approx 0.2614972128$ is the Meissel-Mertens constant. The Robin theorem states that $\delta(x)$ changes sign infinitely often. Let's also define $S(x) = \theta(x)-x$, where $\theta(x)$ is the Chebyshev function. It is known that $S(x)$ changes sign infinitely often. We define the another function $\varpi(x)=\left(\sum_{{q\leq x}}{\frac{1}{q}}-\log\log \theta(x)-B \right)$. We prove that when the inequality $\varpi(x)\leq 0$ is satisfied for some number $x\geq 3$, then the Riemann hypothesis should be false. The Riemann hypothesis is also false when the inequalities $\delta(x)\leq 0$ and $S(x)\geq 0$ are satisfied for some number $x\geq 3$ or when $\frac{3\times\log x+5}{8\times\pi\times\sqrt{x}+1.2\times\log x+2}+\frac{\log x}{\log\theta(x)}\leq 1$ is satisfied for some number $x\geq 13.1$ or when there exists some number $y\geq 13.1$ such that for all $x\geq y$ the inequality $\frac{3\times\log x+5}{8\times \pi \times\sqrt{x}+1.2 \times\log x+2}+\frac{\log x}{\log(x+C \times\sqrt{x} \times \log\log\log x)}\leq 1$ is always satisfied for some positive constant $C$ independent of $x$.

[24] Observe how implausible his claim is. He assessed his whole property at a value of two hundred and fifty drachmas. Now it would be remarkable if he hired a male lover for more money than he actually possesses. [25] But his impudence is such that he is not content to lie merely about this point, the payment of the money; he actually says that he has been repaid. But surely it’s inconceivable that at that point we would commit offences of the sort he has charged us with, in an attempt to deprive him of the three hundred drachmas, and pay back the money precisely when we had outfought him, without obtaining formal release from his charges and when under no compulsion? [26] No, Council, all this is a calculated fabrication by him; he says he gave the money so that he will not seem guilty of intolerable conduct in daring to treat the lad so outrageously when there was no compact between them, and he pretends to have been repaid because it is obvious that he never made a formal complaint about money or made any mention of it whatsoever. [27] And he claims that he was beaten and left in a terrible condition by me at his own door. Yet it is certain that he pursued the boy more than four stades from his house without any injury, and he denies this though more than two hundred people saw it. [28] He says that we came to his house with shards of pottery and I threatened to kill him; and this indicates intent. In my opinion, Council, it is easy to tell that he is lying, not only for you who regularly consider such matters but for the rest of the world as well. [29] Who could find it credible that with full intent and deliberation I came to Simon’s house in the daytime, with the lad, when there was such a large number of people gathered there, unless I was so deranged as to wish to fight alone against large numbers? Besides which, I knew that he would be delighted to see me at his door, since it was he who used to come to my house and force his way in, and who had the impudence to search for me without any consideration for my sister and my nieces, and finding out where I happened to be at dinner called me out and hit me. [30] And at that point, it seems, I kept my peace to avoid notoriety, regarding his criminality as my misfortune, but when time had passed, I then (according to him) became eager for notoriety! [31] If the boy had been at his house, it would make some sense for him to lie to the effect that I was compelled by desire to behave somewhat more foolishly than usual. As it stands, the boy would not even talk to him, but hated him more than anyone in the world, while it was with me that he was

2002 ◽  
pp. 87-87
Keyword(s):  
A Value ◽  
Large Numbers ◽  
The World ◽  
Formal Complaint ◽  
To Come

scholarly journals Prediksi Harga Kontrak Opsi Asia dalam Perdagangan Pasar Saham dengan Menggunakan Metode Monte Carlo

2019 ◽  
Vol 1 (1) ◽  
pp. 31
Author(s):  
Rahmat Syam ◽  
Ahmad Zaki ◽  
Muhammad Hasriyadi Basri
Keyword(s):  
Monte Carlo ◽  
Predictive Value ◽  
Random Variable ◽  
Stock Option ◽  
Random Numbers ◽  
Option Prices ◽  
A Value ◽  
Large Numbers ◽  
The Monte Carlo Method ◽  
Black Scholes

Abstrak: Opsi adalah suatu kontrak yang memberikan hak (bukan kewajiban) kepada pemegang kontrak (option buyer) untuk membeli atau menjual suatu aset tertentu suatu perusahaan kepada penulis opsi (option writer). Apabila pada saat jatuh tempo (expiration date) pemegang opsi tidak menggunakan haknya, maka hak tersebut akan hilang dengan sendirinya. Dengan demikian opsi yang dimiliki tidak akan mempunyai nilai lagi. Monte Carlo adalah suatu metode yang menghendaki model simulasi yang mengikutsertakan bilangan acak dan sampel yang berbasis pada komputer. Prosedur simulasi melibatkan pembangkit bilangan acak dengan memberikan kepadatan probabilitas dan menggunakan hukum bilangan besar untuk mendapatkan rata-rata dari nilainya sebagai penaksir dari nilai harapan variabel acak. Penelitian ini bertujuan untuk memprediksi harga opsi saham pada periode kedepannya dan sebagai bahan pertimbangan bagi pelaku perdagangan saham untuk mengambul keputusan untuk menjual atau membali opsi suatu saham dengan menggunakan software Matlab. Jenis penelitian yang digunakan adalah penelitian terapan menggunakan metode Monte Carlo untuk mensimulasikan data saham. Hasil menunjukkan bahwa semakin banyak iterasi yang dilakukan maka nilai prediksi juga semakin baik dan konvergen ke suatu nilai. Nilai prediksi stabil pada iterasi ke-60000 dengan nilai error dari MAPE kurang dari 20% sehingga nilai prediksi dapat dikatakan baik.Kata Kunci: Opsi Asia, Monte Carlo, Black-Scholes, Matlab, MAPE.Abstract: Option is a contract that gives rights (not obligations) to the contract holder (option buyer) to buy or sell a certain asset of a company to the option writer (option writer). Monte Carlo is a method that requires a simulation model that includes random numbers and samples based on computers. The simulation procedure involves generating random numbers by providing a probability density and using the law of large numbers to get the average of its values as an estimator of the expected value of the random variable. This study aims to predict stock option prices in the future and as a material consideration for stock trading players to make a decision to sell or buy options for a stock using Matlab software. The type of research used is applied research using the Monte Carlo method to simulate stock data. The results show that the more iterations are carried out, the predictive value is also getting better and converging to a value. The predictive value is stable at the 60000th iteration with an error value of MAPE of less than 20% so that the predicted value can be said to be good.Keywords: Asia Option, Monte Carlo, Black-Scholes, Matlab, MAPE.

scholarly journals A PROBLEM OF FOMENKO'S RELATED TO ARTIN'S CONJECTURE

2012 ◽  
Vol 08 (07) ◽  
pp. 1687-1723 ◽  
Author(s):  
ADAM TYLER FELIX ◽  
M. RAM MURTY
Keyword(s):  
Natural Number ◽  
Positive Constant ◽  
Riemann Hypothesis ◽  
Generalized Riemann Hypothesis ◽  
Average Value ◽  
Artin's Conjecture

Let a be a natural number greater than 1. For each prime p, let ia(p) denote the index of the group generated by a in [Formula: see text]. Assuming the generalized Riemann hypothesis and Conjecture A of Hooley, Fomenko proved in 2004 that the average value of ia(p) is constant. We prove that the average value of ia(p) is constant without using Conjecture A of Hooley. More precisely, we show upon GRH that for any α with 0 ≤ α < 1, there is a positive constant cα > 0 such that [Formula: see text] where π(x) is the number of primes p ≤ x. We also study related questions.

Cytoplasmic Granules in Lymphocytes from Rats Dosed with SK&F 14336-D

1971 ◽  
Vol 29 ◽  
pp. 556-557
Author(s):  
T. G. Merrill ◽  
B. J. Payne ◽  
A. J. Tousimis
Keyword(s):  
Lipid Storage ◽  
Pokeweed Mitogen ◽  
Electron Microscopic ◽  
Cytoplasmic Granules ◽  
Storage Diseases ◽  
Tay Sachs Disease ◽  
Large Numbers ◽  
Microscopic Studies ◽  
Neurovisceral Lipidosis

Rats given SK&F 14336-D (9-[3-Dimethylamino propyl]-2-chloroacridane), a tranquilizing drug, developed an increased number of vacuolated lymphocytes as observed by light microscopy. Vacuoles in peripheral blood of rats and humans apparently are rare and are not usually reported in differential counts. Transforming agents such as phytohemagglutinin and pokeweed mitogen induce similar vacuoles in in vitro cultures of lymphocytes. These vacuoles have also been reported in some of the lipid-storage diseases of humans such as amaurotic familial idiocy, familial neurovisceral lipidosis, lipomucopolysaccharidosis and sphingomyelinosis. Electron microscopic studies of Tay-Sachs' disease and of chloroquine treated swine have demonstrated large numbers of “membranous cytoplasmic granules” in the cytoplasm of neurons, in addition to lymphocytes. The present study was undertaken with the purpose of characterizing the membranous inclusions and developing an experimental animal model which may be used for the study of lipid storage diseases.

Prolonged Fixation Studies For Spaceflight

1973 ◽  
Vol 31 ◽  
pp. 332-333
Author(s):  
Robert Corbett ◽  
Delbert E. Philpott ◽  
Sam Black
Keyword(s):  
High Pressure ◽  
Living Systems ◽  
Prolonged Storage ◽  
Time Intervals ◽  
Early Signs ◽  
Large Numbers

Observation of subtle or early signs of change in spaceflight induced alterations on living systems require precise methods of sampling. In-flight analysis would be preferable but constraints of time, equipment, personnel and cost dictate the necessity for prolonged storage before retrieval. Because of this, various tissues have been stored in fixatives and combinations of fixatives and observed at various time intervals. High pressure and the effect of buffer alone have also been tried.Of the various tissues embedded, muscle, cartilage and liver, liver has been the most extensively studied because it contains large numbers of organelles common to all tissues (Fig. 1).

Analysis of the Anterior Secretory Cells of Onchidohs Muricata (Nudibranchia)

1981 ◽  
Vol 39 ◽  
pp. 614-615
Author(s):  
Roy Skidmore
Keyword(s):  
Endoplasmic Reticulum ◽  
Secretory Granules ◽  
Golgi Body ◽  
The Body ◽  
Secretory Cells ◽  
Secretory Vesicles ◽  
High Magnification ◽  
Large Numbers ◽  
Membrane Bound ◽  
Sole Of The Foot

The long-necked secretory cells in Onchidoris muricata are distributed in the anterior sole of the foot. These cells are interspersed among ciliated columnar and conical cells as well as short-necked secretory gland cells. The long-necked cells contribute a significant amount of mucoid materials to the slime on which the nudibranch travels. The body of these cells is found in the subepidermal tissues. A long process extends across the basal lamina and in between cells of the epidermis to the surface of the foot. The secretory granules travel along the process and their contents are expelled by exocytosis at the foot surface.The contents of the cell body include the nucleus, some endoplasmic reticulum, and an extensive Golgi body with large numbers of secretory vesicles (Fig. 1). The secretory vesicles are membrane bound and contain a fibrillar matrix. At high magnification the similarity of the contents in the Golgi saccules and the secretory vesicles becomes apparent (Fig. 2).

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