搜索结果：Glasnik (Srpska akademija nauka)

This book is devoted to finite-dimensional problems of non-convex non-smooth optimization and numerical methods for their solution. The problem of nonconvexity is studied in the book on two main models of nonconvex dependencies: these are the so-called generalized differentiable functions and locally Lipschitz functions. Non-smooth functions naturally arise in various applications. In addition, they often appear in the theory of extremal problems itself due to the operations of taking the maximum and minimum, decomposition techniques, exact non-smooth penalties, and duality. The considered models of nonconvexity are quite general and cover the majority of practically important optimization problems; they clearly show all the difficulties of non-convex optimization. The method of studying the generalized differentiable functions is that for these functions a generalization of the concept of gradient is introduced, a calculus is constructed, and various properties of nonconvex problems are studied in terms of generalized gradients. As for numerical methods, it is possible to extend the theory and algorithms of subgradient descent of convex optimization to problems with generalized di

Left-invariant Hermitian and Gauduchon connections are studied on an arbitrary Lie group $G$ equipped with an arbitrary left-invariant almost Hermitian structure $(\langle\cdot,\cdot\rangle,J)$. The space of left-invariant Hermitian connections is shown to be in one-to-one correspondence with the space $\wedge^{(1,1)}\mathfrak{g}^\ast\otimes \mathfrak{g}$ of left-invariant 2-forms of type (1,1) (with respect to $J$) with values in $\mathfrak{g}:=\mbox{Lie}(G)$. Explicit formulas are obtained for the torsion components of every Hermitian and Gauduchon connection with respect to a convenient choice of left-invariant frame on $G$. The curvature of Gauduchon connections is studied for the special case $G=H\times A$, where $H$ is an arbitrary $n$-dimensional Lie group, $A$ is an arbitrary $n$-dimensional abelian Lie group, and the almost complex structure is totally real with respect to $\mathfrak{h}:=\mbox{Lie}(H)$. When $H$ is compact, it is shown that $H\times A$ admits a left-invariant (strictly) almost Hermitian structure $(\langle\cdot,\cdot\rangle,J)$ such that the Gauduchon connection corresponding to the Strominger (or Bismut) connection in the integrable case is precisely the

After the loss of control authority over thrusters of the Nauka module, the International Space Station lost attitude control for 45 minutes with potentially disastrous consequences. Motivated by a scenario of orbital inspection, we consider a similar malfunction occurring to the inspector satellite and investigate whether its mission can still be safely fulfilled. While a natural approach is to counteract in real-time the uncontrolled and undesirable thrust with the remaining controlled thrusters, vehicles are often subject to actuation delays hindering this approach. Instead, we extend resilience theory to systems suffering from actuation delay and build a resilient trajectory tracking controller with stability guarantees relying on a state predictor. We demonstrate that this controller can track accurately the reference trajectory of the inspection mission despite the actuation delay and the loss of control authority over one of the thrusters.

In 1985, Janko and Tran Van Trung published an algorithm for constructing symmetric designs with prescribed automorphisms. This algorithm is based on the equations by Dembowski (1958) for tactical decompositions of point-block incidence matrices. In the sequel, the algorithm has been generalized and improved in many articles. In parallel, higher incidence matrices have been introduced by Wilson in 1982. They have proven useful for obtaining several restrictions on the existence of designs. For example, a short proof of the generalized Fisher's inequality makes use of these incidence matrices. In this paper, we introduce a unified approach to tactical decompositions and incidence matrices. It works for both combinatorial and subspace designs alike. As a result, we obtain a generalized Fisher's inequality for tactical decompositions of combinatorial and subspace designs. Moreover, our approach is explored for the construction of combinatorial and subspace designs of arbitrary strength.

Let $d$ be a square-free integer and $\mathbb{Z}[\sqrt{d}]$ a quadratic ring of integers. For a given $n\in\mathbb{Z}[\sqrt{d}]$, a set of $m$ non-zero distinct elements in $\mathbb{Z}[\sqrt{d}]$ is called a Diophantine $D(n)$-$m$-tuple (or simply $D(n)$-$m$-tuple) in $\mathbb{Z}[\sqrt{d}]$ if product of any two of them plus $n$ is a square in $\mathbb{Z}[\sqrt{d}]$. Assume that $d \equiv 2 \pmod 4$ is a positive integer such that $x^2 - dy^2 = -1$ and $x^2 - dy^2 = 6$ are solvable in integers. In this paper, we prove the existence of infinitely many $D(n)$-quadruples in $\mathbb{Z}[\sqrt{d}]$ for $n = 4m + 4k\sqrt{d}$ with $m, k \in \mathbb{Z}$ satisfying $m ot\equiv 5 \pmod{6}$ and $k ot\equiv 3 \pmod{6}$. Moreover, we prove the same for $n = (4m + 2) + 4k\sqrt{d}$ when either $m ot\equiv 9 \pmod{12}$ and $k ot\equiv 3 \pmod{6}$, or $m ot\equiv 0 \pmod{12}$ and $k ot\equiv 0 \pmod{6}$. At the end, some examples supporting the existence of quadruples in $\mathbb{Z}[\sqrt{d}]$ with the property $D(n)$ for the above exceptional $n$'s are provided for $d = 10$.

After a loss of control authority over thrusters of the Nauka module, the International Space Station lost attitude control for 45 minutes with potentially disastrous consequences. Motivated by this scenario, we investigate the continued capability of control systems to perform their task despite partial loss of authority over their actuators. We say that a system is resilient to such a malfunction if for any undesirable inputs and any target state there exists an admissible control driving the state to the target. Building on controllability conditions and differential games theory, we establish a necessary and sufficient condition for the resilience of linear systems. As their task might be time-constrained, ensuring completion alone is not sufficient. We also want to estimate how much slower the malfunctioning system is compared to its nominal performance. Relying on Lyapunov theory we derive analytical bounds on the reach times of the nominal and malfunctioning systems in order to quantify their resilience. We illustrate our work on the ADMIRE fighter jet model and on a temperature control system.

Let $ \{F_n\}_{n\ge 0} $ be the sequence of Fibonacci numbers and let $p$ be a prime. For an integer $c$ we write $m_{F,p}(c)$ for the number of distinct representations of $c$ as $F_k-p^\ell$ with $k\ge 2$ and $\ell\ge 0$. We prove that $m_{F,p}(c)\le 4$.

In this paper we study the polynomial version of Pillai's conjecture on the exponential Diophantine equation \begin{equation*} p^n - q^m = f. \end{equation*} We prove that for any non-constant polynomial $ f $ there are only finitely many vectors $ (n,m,\mathrm{deg}\ p,\mathrm{deg}\ q) $ with integers $ n,m \geq 2 $ and non-constant polynomials $ p,q $ such that Pillai's equation holds. Moreover, we will give some examples that there can still be infinitely many possibilities for the polynomials $ p,q $.

A long-overlooked organ may hold surprising clues to healthy aging and cancer survival。 Researchers at Mass General Brigham used AI to analyze CT scans from tens of thousands of adults and found that people with healthier thymuses—a small immune-system organ once thought to become largely irrelevant after childhood—lived longer and had substantiall

The chances are low, but not zero

Scientists have developed a solar desalination system that turns seawater into drinking water without creating environmentally damaging brine。 Special laser-textured metal panels use sunlight to evaporate water while automatically moving salt deposits away from the working surface, preventing clogging。 The process was successfully tested with water

NASA’s PExT terminal has shown that spacecraft can seamlessly communicate through multiple government and commercial networks, a major step beyond traditional single-network systems。 The mission is now expanding to test new capabilities that could help create a more flexible, reliable communications infrastructure for future space missions

NASA says a long-running air leak aboard the ISS recently worsened, leading engineers to investigate new suspected crack locations and consider a riskier repair strategy。 Astronauts were temporarily moved into a safe haven as a precaution before the repair was postponed for further analysis

Researchers gave top AI models a classic attention test used in psychology and found a major flaw。 While the models could correctly name colors in short lists, their performance deteriorated sharply as the task became longer and more complex。 Some leading systems fell from over 90% accuracy to nearly complete failure

Researchers have discovered how microscopic imperfections and atomic vibrations can be used to control a powerful quantum effect in an advanced material。 The effect can turn alternating electrical signals from the environment directly into the kind of current electronic devices need, without traditional components。 As temperature changes, the signa

Some models run in Google's cloud, but without giving Google any kind of access

NASA’s Roman Space Telescope could revolutionize the search for alien worlds by discovering around 100,000 exoplanets—far more than all previous missions combined。 It will look deep into unexplored parts of the Milky Way, helping scientists compare planetary systems across very different galactic environments。 The mission will also uncover rare Ear

Five peer-reviewed papers update the design and model its expected output

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