On the S-procedure and some variants

We give a concise review and extension of S-procedure that is an instrumental tool in control theory and robust optimization analysis. We also discuss the approximate S-Lemma as well as its applications in robust optimization

On the s-procedure and some variants

Cataloged from PDF version of article.In this thesis, we deal with the S-procedure that corresponds to verifying that the minimum of a quadratic function over constraints consisting of quadratic functions is positive. S-procedure is an instrumental tool in control theory and robust optimization analysis. It is also used in linear matrix inequality (or semi definite programming) reformulations and analysis of quadratic programming. We improve an error bound in the Approximate S-Lemma used in establishing levels of conservatism results for approximate robust counterparts. Moreover we extend the S-procedure and obtain some general results in this field. Finally, we get a bound similar to Nesterov’s bound for trust region subproblem, which consists in minimizing an indefinite quadratic function subject to a norm-1 constraint by using the Approximate S-Lemma.Derinkuyu, KürşadM.S

In-mould decoration

Izgled injekcijski prešanoga otpreska trajno dobiva na važnosti. Postizanju željenoga izgleda pridonose sve prošireniji postupci injekcijskoga ukrašavanja gdje se otpresak djelomično ili potpuno prekriva ukrasnim (dekoracijskim) slojem unutar jednoga radnog ciklusa. Opisani su postupci injekcijskoga ukrašavanja pripremkom: etiketom, pripremcima s naličem i laminatom. Upozoreno je na neke suvremene postupke: Decoform i Decopress. Prikazani su primjeri etiketiranja injekcijskoga prešanja iz jedne hrvatske tvornice.The appearance of injection moulded parts has been gaining more and more in importance. In-mould decoration can help to reach this goal. Some of in-mould decoration technologies are described. These are in-mould labelling, painting and lamination. The attention is called to some modern variants of injection moulding decoration: Decoform and Decopress. The examples of using in-mould labelling are given based on the introduction of this procedure in one Croatian company

Gauge invariance and radiative corrections in an extra dimensional theory

The gauge structure of the four dimensional effective theory originated in a pure five dimensional Yang-Mills theory compactified on the orbifold $S^1/Z_2$, is discussed on the basis of the BRST symmetry. If gauge parameters propagate in the bulk, the excited Kaluza-Klein (KK) modes are gauge fields and the four dimensional theory is gauge invariant only if the compactification is carried out by using curvatures as fundamental objects. The four dimensional theory is governed by two types of gauge transformations, one determined by the KK zero modes of the gauge parameters and the other by the excited ones. Within this context, a gauge-fixing procedure to quantize the KK modes that is covariant under the first type of gauge transformations is shown and the ghost sector induced by the gauge-fixing functions is presented. If the gauge parameters are confined to the usual four dimensional space-time, the known result in the literature is reproduced with some minor variants, although it is emphasized that the excited KK modes are not gauge fields, but matter fields transforming under the adjoint representation of $SU_4(N)$. A calculation of the one-loop contributions of the excited KK modes of the electroweak gauge group on the off-shell WWV, with V a photon or a Z boson, is exhibited. Such contributions are free of ultraviolet divergences and well-behaved at high energies.Comment: 7 pages, conference proceedings, a new reference was added, the title has been change

Glaserian Grounded Theory and Straussian Grounded Theory: Two Standard Qualitative Research Approaches in Social Science

Grounded theory (GT) has appeared as a popular research approach in many branches of social science that acts for the well-being of the society. It is an inductive methodology, and focuses on the discovery of theory from data. Overtimes original grounded theory of Barney Galland Glaser (1930-2022) and Anselm Leonard Strauss (1916-1996) has evolved, and two grounded theory variants: Glaserian grounded theory and Straussian grounded theory have been emerged as qualitative approaches. When a novice qualitative researcher starts data collection on grounded theory; s/he cannot identify the differences between the two approaches. In this paper some of the key differences and similarities of the two methods are illustrated. So that, a confused researcher can easily selects the desired grounded theory for his/her research version. In this study an attempt has been taken to continue the grounded theory research smoothly when the novice researchers face uncertainty during the research procedure

Some topics in process planning of rotational turning

There could be different procedure variants of chip removal by the applied kinematic relations in turning operations. Recently, some research and analysis of these variants have come to the front since turning can replace grinding in precision machining operations due to the development of tools with geometrically defined cutting edge(s) and tool materials, even in machining of hardened surfaces. This frequently occurs in finish machining, therefore the application of the topography meeting the functional requirements best and also the procedure leading to that has become crucially important. Some of the technological issues of one of the variants – rotational turning – is the subject of this work. Rotational turning does the cutting with a long, oblique and spatial positioned cutting edge instead of the single-point cutting tools applied in traditional turning. The slow rotation of the cutting edge on a large diameter causes a skiving-like material removal mechanism. In order to calculate the cutting parameters as well as to determine the machining times and the productivity, the rotation angles of the tool needed for the run-in, run-out and the constant phases must be known. In this paper the rotation angles based on geometrical conditions are determined and a method for their calculation is given. The structure of the applied tool and the applicable technological parameters are described and in addition, the high productivity of this procedure is shown. Finally, the method for determining the cutting parameters is described

SLOPE - Adaptive variable selection via convex optimization

We introduce a new estimator for the vector of coefficients $\beta$ in the linear model $y=X\beta+z$, where $X$ has dimensions $n\times p$ with $p$ possibly larger than $n$. SLOPE, short for Sorted L-One Penalized Estimation, is the solution to $$\min_{b\in\mathbb{R}^p}\frac{1}{2}\Vert y-Xb\Vert _{\ell_2}^2+\lambda_1\vert b\vert _{(1)}+\lambda_2\vert b\vert_{(2)}+\cdots+\lambda_p\vert b\vert_{(p)},$$ where $\lambda_1\ge\lambda_2\ge\cdots\ge\lambda_p\ge0$ and $\vert b\vert_{(1)}\ge\vert b\vert_{(2)}\ge\cdots\ge\vert b\vert_{(p)}$ are the decreasing absolute values of the entries of $b$. This is a convex program and we demonstrate a solution algorithm whose computational complexity is roughly comparable to that of classical $\ell_1$ procedures such as the Lasso. Here, the regularizer is a sorted $\ell_1$ norm, which penalizes the regression coefficients according to their rank: the higher the rank - that is, stronger the signal - the larger the penalty. This is similar to the Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289-300] procedure (BH) which compares more significant $p$-values with more stringent thresholds. One notable choice of the sequence $\{\lambda_i\}$ is given by the BH critical values $\lambda_{\mathrm {BH}}(i)=z(1-i\cdot q/2p)$, where $q\in(0,1)$ and $z(\alpha)$ is the quantile of a standard normal distribution. SLOPE aims to provide finite sample guarantees on the selected model; of special interest is the false discovery rate (FDR), defined as the expected proportion of irrelevant regressors among all selected predictors. Under orthogonal designs, SLOPE with $\lambda_{\mathrm{BH}}$ provably controls FDR at level $q$. Moreover, it also appears to have appreciable inferential properties under more general designs $X$ while having substantial power, as demonstrated in a series of experiments running on both simulated and real data.Comment: Published at http://dx.doi.org/10.1214/15-AOAS842 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org