Assessment of natural density of distribution for fish by the catches at light stations by Oleg N. Kruchinin, Michael А. Mizyurkin, Yury V. Eremin, Nikita L. Wacker

“…Relationship between natural density of saury distribution and its catch per trap is determined for this trap.…”
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On the Natural Density of Sets Related to Generalized Fibonacci Numbers of Order <i>r</i> by Pavel Trojovský

Subjects: “…natural density…”
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A demo‐genetic model shows how silviculture reduces natural density‐dependent selection in tree populations by Claire Godineau, Victor Fririon, Nicolas Beudez, François deColigny, François Courbet, Gauthier Ligot, Sylvie Oddou‐Muratorio, Leopoldo Sanchez, François Lefèvre

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STATISTICAL BOUNDED SEQUENCES OF BI-COMPLEX NUMBERS by S. Bera, B. Ch. Tripathy

Subjects: “…natural density…”
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The Proof of a Conjecture Related to Divisibility Properties of <i>z</i>(<i>n</i>) by Eva Trojovská, Kandasamy Venkatachalam

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On the Parity of the Order of Appearance in the Fibonacci Sequence by Pavel Trojovský

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The Proof of a Conjecture on the Density of Sets Related to Divisibility Properties of <i>z</i>(<i>n</i>) by Eva Trojovská, Venkatachalam Kandasamy

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On Some Properties of the Limit Points of (<i>z</i>(<i>n</i>)/<i>n</i>)_<i>n</i> by Eva Trojovská, Kandasamy Venkatachalam

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Chlodowsky type $\left( \lambda,q\right)$-Bernstein Stancu operators of Pascal rough triple sequences by Ayhan Esi, Subramanian Nagarajan, Kemal Ozdemir

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Sums of two squares are strongly biased towards quadratic residues by Gorodetsky, O

“…To illustrate, we have under GRH that the number of sums of two squares up to&nbsp;<span tabindex="0">x</span>&nbsp;that are&nbsp;<span tabindex="0">1mod3</span>&nbsp;is greater than those that are&nbsp;<span tabindex="0">2mod3</span>&nbsp;100% of the time in natural density sense.</p>…”

The density of shifted and affine Eisenstein polynomials by Micheli, G, Schnyder, R

“…In this paper we provide a complete answer to a question by Heyman and Shparlinski concerning the natural density of polynomials which are irreducible by Eisenstein's criterion after applying some shift. …”

Evolution of flowering decisions in a stochastic, density-dependent environment. by Metcalf, C, Rose, K, Childs, D, Sheppard, A, Grubb, P, Rees, M

“…Here, we show how, by combining a range of theoretical approaches with the statistical analysis of individually structured databases, accurate prediction of life history decisions is possible in natural density-regulated populations undergoing large fluctuations in demographic rates from year to year. …”

SIGN PATTERNS OF THE LIOUVILLE AND MÖBIUS FUNCTIONS by KAISA MATOMÄKI, MAKSYM RADZIWIŁŁ, TERENCE TAO

“…By using the recent result of the first two authors on mean values of multiplicative functions in short intervals, we strengthen Hildebrand’s result by proving that each of these eight sign patterns occur with positive lower natural density. We also obtain an analogous result for the nine possible sign patterns for $({\it\mu}(n),{\it\mu}(n+1))$ . …”
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In Silico Studies on Selected Neutral Molecules, CGa₂Ge₂, CAlGaGe₂, and CSiGa₂Ge Containing Planar Tetracoordinate Carbon by Prasenjit Das, Pratim Kumar Chattaraj

“…The nature of bonding is understood through the adaptive natural density partitioning analysis (AdNDP), quantum theory of atoms in molecules (QTAIM) analysis, and also via Wiberg bond index (WBI) and electron localization function (ELF).…”
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Occurrence of Double Bond in <i>π</i>-Aromatic Rings: An Easy Way to Design Doubly Aromatic Carbon-Metal Structures by Nikolay V. Tkachenko, Alvaro Muñoz-Castro, Alexander I. Boldyrev

“…A chemical bonding of several metallabenzenes and metallabenzynes was studied via an adaptive natural density partitioning (AdNDP) algorithm and the induced magnetic field analysis. …”
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neuroAIx-Framework: design of future neuroscience simulation systems exhibiting execution of the cortical microcircuit model 20× faster than biological real-time by Kevin Kauth, Tim Stadtmann, Vida Sobhani, Tobias Gemmeke

“…With real-time capabilities surpassed for established models like the cortical microcircuit, it is time to conceive next-generation systems: neuroscience simulators providing significant acceleration, even for larger networks with natural density, biologically plausible multi-compartment models and the modeling of long-term and structural plasticity.MethodsStressing the need for agility to adapt to new concepts or findings in the domain of neuroscience, we have developed the neuroAIx-Framework consisting of an empirical modeling tool, a virtual prototype, and a cluster of FPGA boards. …”
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Möbius formulas for densities of sets of prime ideals by Kural, Michael, McDonald, Vaughan, Sah, Ashwin

“…We show that if K is a number field and S is any set of prime ideals with natural density $$\delta (S)$$δ(S) within the primes, then $$\begin{aligned} -\lim _{X \rightarrow \infty }\sum _{\begin{array}{c} 2 \le {\text {N}}(\mathfrak {a})\le X\\ \mathfrak {a} \in D(K,S) \end{array}}\frac{\mu (\mathfrak {a})}{{\text {N}}(\mathfrak {a})} = \delta (S), \end{aligned}$$-limX→∞∑2≤N(a)≤Xa∈D(K,S)μ(a)N(a)=δ(S),where $$\mu (\mathfrak {a})$$μ(a) is the generalized Möbius function and D(K, S) is the set of integral ideals $$ \mathfrak {a} \subseteq \mathcal {O}_K$$a⊆OK with unique prime divisor of minimal norm lying in S. …”
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A Study on The Effect of Temperature on Human Prion Protein Structure through Molecular Dynamic Simulation by Fatemeh Khajavi, Mohamad Reza Dayer

“…The results of this study show that, with 0.1 molar sodium chloride (natural density in tissues), a change in the temperature of environment from 37 ℃ (natural temperature of the body) to 27 ℃ or 47 ℃ leads to structural changes. …”
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Almost all orbits of the Collatz map attain almost bounded values by Terence Tao

“…Previously, it was shown by Korec that for any $\theta> \frac {\log 3}{\log 4} \approx 0.7924$ , one has ${\operatorname {Col}}_{\min }(N) \leq N^\theta $ for almost all $N \in \mathbb {N}+1$ (in the sense of natural density). In this paper, we show that for any function $f \colon \mathbb {N}+1 \to \mathbb {R}$ with $\lim _{N \to \infty } f(N)=+\infty $ , one has ${\operatorname {Col}}_{\min }(N) \leq f(N)$ for almost all $N \in \mathbb {N}+1$ (in the sense of logarithmic density). …”
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Effects of sandfish (Holothuria scabra) removal on shallow-water sediments in Fiji by Steven Lee, Amanda K. Ford, Sangeeta Mangubhai, Christian Wild, Sebastian C.A. Ferse

“…Three treatments were investigated: (i) high density (350 g m−2 wet weight; ca. 15 individuals); (ii) natural density (60 g m−2; ca. 3 individuals); and (iii) exclusion (0 g m−2). …”
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