Local-moves on knots and products of knots II

We use the terms, knot product and local-move, as defined in the text of this paper. Let [Formula: see text] be an integer [Formula: see text]. Let [Formula: see text] be the set of simple spherical [Formula: see text]-knots in [Formula: see text]. Let [Formula: see text] be an integer [Formula: see text]. We prove that the map [Formula: see text] is bijective, where [Formula: see text]Hopf, and Hopf denotes the Hopf link. Let [Formula: see text] and [Formula: see text] be 1-links in [Formula: see text]. Suppose that [Formula: see text] is obtained from [Formula: see text] by a single pass-move, which is a local-move on 1-links. Let [Formula: see text] be a positive integer. Let [Formula: see text] denote the knot product [Formula: see text]. We prove the following: The [Formula: see text]-dimensional submanifold [Formula: see text] [Formula: see text] is obtained from [Formula: see text] by a single [Formula: see text]-pass-move, which is a local-move on [Formula: see text]-submanifolds contained in [Formula: see text]. See the body of this paper for the definitions of all local-moves in this abstract. We prove the following: Let [Formula: see text], and [Formula: see text] be positive integers. If the [Formula: see text] torus link is pass-move-equivalent to the [Formula: see text] torus link, then the Brieskorn manifolds, [Formula: see text] and [Formula: see text], are diffeomorphic as abstract manifolds. Let [Formula: see text] and [Formula: see text] be (not necessarily connected or spherical) 2-dimensional closed oriented submanifolds in [Formula: see text]. Suppose that [Formula: see text] is obtained from [Formula: see text] by a single ribbon-move, which is a local-move on 2-dimensional submanifolds contained in [Formula: see text]. Let [Formula: see text] be an integer [Formula: see text]. We prove the following: The [Formula: see text]-submanifold [Formula: see text] [Formula: see text] is obtained from [Formula: see text] by a single [Formula: see text]-pass-move, which is a local-move on [Formula: see text]-dimensional submanifolds contained in [Formula: see text].

Uji Efektivitas Antibakteri Sediaan Salep Ekstrak Daun Puring (Codiaeum variegatum (L.) Rumph. Ex A.Juss) Terhadap Bakteri Staphylococus aureus

Indonesia is one of the rich countries among the plant’s potential medicinal properties is the puring leaf (Codiaem variegatum (L.) Rumph. Ex A.Jus) as an antibacterial. The puring leaves contain flavonoid, steroids, alkaloids, tannins, saponins and fenols. which serve as antibacterial. The use of antibacterial ointments can treat bacterial skin infections. Balm is a half-denser is intended for topical wear on the skin or the mucous membranes. Among the causes of infection is the Staphylococus aureus bacteria. The study aims to test the effectiveness of a suppressive antibacterias, the leaf extract ointment against the Staphylococus aureus bacteria. Extraction methods maceration method use a 96% solution. The research method used was oriental. The extract of the puring leaves used is 2,5%, 5%, 7,5%, 10%, the negative cotrol of the ointment without the extract and the positive control with the gentamicin ointment. Zone research is inhibiting every single formula. Averag buffer zone on formula 1 6.25 mm, formula 2 7.55 mm, formula 3 9.23 mm and formula 4 11.68 mm. Data acquired by the formation of a clear buffer zone around the commonwealth for 24 hours after treatment. The data was analyzed with one way ANOVA continues the post hoc test (Tukey). The result is that partial extract of puring leave can be made into unguent and effective Staphylocous aureus ATCC 25923Keywords: Extract of puring leaves; antibacterial; ointment and staphylococus aureus AbstrakIndonesia merupakan salah satu negara yang kaya akan keaneragaman tanaman yang memiliki potensi sebagai bahan obat, salah satunya yaitu daun puring (Codiaeum variegatum (L.) Rumph. Ex A.Juss) sebagai antibakteri. Daun puring memiliki senyawa flavonoid, steroid, alkaloid, tannin, saponin dan fenol yang berfungsi sebagai antibakteri. Penggunaan salep antibakteri dapat mengobati infeksi kulit yang disebabkan oleh bakteri. Salep merupakan sediaan setengah padat yang ditujukan untuk pemakaian topikal pada kulit atau selaput lendir. Salah satu penyebab infeksi adalah bakteri Staphylococcus aureus. Penelitian ini bertujuan untuk menguji efektivitas antibakteri sediaan salep ekstrak daun puring terhadap bakteri Staphylococus aureus. Metode ekstraksi menggunakan metode maserasi dengan pelarut 96%. Metode penelitian yang digunakan yaitu sumuran. Konsentrasi ekstrak daun puring yang digunakan adalah 2,5%, 5%, 7,5%, 10%, kontrol negatif yaitu salep tanpa ekstrak dan kontrol positif dengan salep gentamicin. Hasil penelitian zona hambat setiap formula berbeda. Rata-rata zona hambat pada formula 1 6,25 mm, formula 2 7,55 mm, formula 3 9,23 mm dan formula 4 11,68 mm. Data yang diperoleh dengan terbentuknya zona hambat bening di sekeliling sumuran selama 24 jam setelah perlakuan. Data dianalisa dengan one way ANOVA dilanjutkan uji post Hoc (Tukey). Kesimpulannya Ekstrak daun puring bisa dibuat sediaan salep dan ekstrak daun puring efektif terhadap bakteri Staphylococus aureus ATCC 25923Kata Kunci: Ekstrak daun puring; antibakteri; salep dan staphylococus aureus

DEVELOPMENT OF METHODS FOR ASSESSING THE SAFETY OF LIGHT HYDROCARBON STORAGE FACILITIES IN EMERGENCY SITUATIONS

The risk of accidents involving light hydrocarbons is caused by the physicochemical properties of the components, primarily propane and butane. The most catastrophic accidents involving these substances were on November 19, 1984, in the city of San Juan Ixhuatepec (Mexico) and on June 4, 1989, on the Asha – Ulu-Telyak section (USSR), in each of which more than 500 people died. The novelty of the study is determined by the requirement to ensure industrial and fire safety of storage facilities for light hydrocarbons by predicting probable zones of air flow stagnation. The authors calculated the formation of probable air stagnation zones for various space-planning solutions by using a three-dimensional modelling system and the finite volume method. The paper developed a methodology for assessing the safety of storage facilities for light hydrocarbons in emergency situations, which is based on the analysis of probable air stagnation zones by using three-dimensional modelling systems. The practical significance of the study is determined by the additional development of a parameter for assessing the safety state of a storage facility for light hydrocarbons (Ks) and a resulting parameter (Kr) for calculating the optimal location of structures and their structural changes. Integration of stagnation zone sizes into a single formula with the results of other safety calculations is an urgent scientific and applied problem.

Incorporating diffusion-weighted imaging in a diagnostic algorithm for multiparametric MR mammography

Background Apparent diffusion coefficient (ADC) measurements are not incorporated in BI-RADS classification. Purpose To assess the probability of malignancy of breast lesions at magnetic resonance mammography (MRM) at 3 T, by combining ADC measurements with the BI-RADS score, in order to improve the specificity of MRM. Material and Methods A total of 296 biopsy-proven breast lesions were included in this prospective study. MRM was performed at 3 T, using a standard protocol with dynamic sequence (DCE-MRI) and an extra echo-planar diffusion-weighted sequence. A freehand region of interest was drawn inside the lesion, and ADC values were calculated. Each lesion was categorized according to the BI-RADS classification. Logistic regression analysis was employed to predict the probability of malignancy of a lesion. The model combined the BI-RADS classification and the ADC value. Sensitivity, specificity, positive predictive value, negative predictive value, and diagnostic accuracy were calculated. Results In total, 153 malignant and 143 benign lesions were analyzed; 257 lesions were masses and 39 lesions were non-mass-like enhancements. The sensitivity and specificity of the combined method were 96% and 86%, respectively, in contrast to 95% and 81% with BI-RADS classification alone. Conclusion We propose a method of assessing the probability of malignancy in breast lesions by combining BI-RADS score and ADC values into a single formula, increasing sensitivity and specificity compared to BI-RADS classification alone.

Polynomial Analogue of Gandy’s Fixed Point Theorem

The paper suggests a general method for proving the fact whether a certain set is p-computable or not. The method is based on a polynomial analogue of the classical Gandy’s fixed point theorem. Classical Gandy’s theorem deals with the extension of a predicate through a special operator ΓΦ(x)Ω∗ and states that the smallest fixed point of this operator is a Σ-set. Our work uses a new type of operator which extends predicates so that the smallest fixed point remains a p-computable set. Moreover, if in the classical Gandy’s fixed point theorem, the special Σ-formula Φ(x¯) is used in the construction of the operator, then a new operator uses special generating families of formulas instead of a single formula. This work opens up broad prospects for the application of the polynomial analogue of Gandy’s theorem in the construction of new types of terms and formulas, in the construction of new data types and programs of polynomial computational complexity in Turing complete languages.

Development of a model of a ground-penetrating radar section of a frozen rock massif with a crack

Revelance of the work. The presence of cracks significantly affects the physical and mechanical properties of rocks, which should be taken into account when planning mining operations and building mining facilities. In the conditions of the spread of permafrost rocks, characteristic of northeastern Russia, the study of fracturing is possible by the GPR method, which is used to assess the structure of rock massifs in placer deposits. The criteria for detecting cracks based on the features of wave georadar fields are currently known, and the main problem that prevents the full use of the georadar method for studying cracks in subsurface layers of rocks is the labour-consuming nature of processing and interpreting data from georadar measurements. Purpose of the work – to determine the patterns of cracks occurrence in frozen rocks in GPR wave fields. Methodology of the work. Based on the results of longstanding field work at the developed areas of alluvial diamond deposits in the Anabar region of the Republic of Sakha (Yakutia), the main elements of the radarogram structure were determined and presented in the form of a single formula. The developed formula is implemented in programs in the SCM Matlab and the results of its execution are compared with the results of modeling in the gprMax system. Results of the work and the scope of their application. The resultant formula describes the main elements of GPR radarograms quite correctly, which confirmed their comparison with the obtained model data. The correlation coefficient between the obtained matrices (Matlab and gprMax) without the low-amplitude values of multiple reflections was 0.91, which shows the identity of the structure of GPR wave fields. Conclusions. The studies carried out have confirmed the possibility of a mathematical description of the ground penetrating radar wave field obtained by sounding a mass of frozen rocks with a crack. The high correlation coefficient showed the adequacy of the developed radarogram model, which will be finalized taking into account the directional diagrams of existing georadars.

CLASSICAL UTILITY OF PANCHATIKTA GUGGULU GHRITA IN ITS INDICATIONS- LITERARY REVIEW

Sneha Kalpanas in Ayurvedic medicine are very effective and unique preparations. In classics, for single formula- tion many indications are stated. For same preparation, some of ingredients are altered in various Samhitas. For a single disease, exact same protocol of treatment cannot be followed. Because treatment protocol will be based on many factors, treatment has to be employed by looking into the involvement of Dosha, Dooshya (tissues) and based on the diseased condition of a patient. In such condition, Yukti (reasoning capacity) of a physician plays important role. Panchatikta Guggulu Ghrita (PTG Ghrita) is one unique formulation which has many indications stated in different Ayurvedic classics. The utility of this medicine can be made by looking into classics thoroughly and analyzing the condition of a patient. PTG Ghrita is indicated in almost all Dhatu and all Srotogata vyadhis (Systemic diseases). PTG Ghrita can be used as Sneha Drava, as a Shodhanaga sneha (oleation in purificatory therapies), as a Shamananga sneha (oleation in Palliative treatment) and also it can be used as Sneha Dravya in Basti dravya (drugs in Enema therapy). Keywords: PTG Ghrita, Panchatikta Guggulu Ghrita, Panchatikta Ghrita Guggulu, Asti-MajjagataVataVikara,

Development and Performance Evaluation of Thin-Layer Color Antiwearing Paving Materials

To develop a color antiwearing wear layer based on epoxy resin adhesives, the effect of single formula composition on the properties of adhesives was analyzed through drawing strength tests, shear strength tests, and bending strength tests. It was found that when the mass ratio of the epoxy resin curing agent and the dosage of the toughening agent increased, the bonding performance and toughness of the adhesive firstly increased and then decreased. With the increase of the mass ratio of phenolic aldehyde amine to polyamide, the bonding performance and toughness of the adhesive were improved, but the effect was significantly reduced when the ratio was more than 2. With the increase of diluent content, the bonding performance and toughness of the adhesive were reduced. Based on response surface optimization, the optimum formulation was recommended. The content of the mass ratio of the epoxy resin to the curing agent and mass ratio of curing agent phenolic amine to polyamide, toughening agent content, and diluent content was determined to be 2.971%, 1.887%, 2.455%, and 1.000%, respectively. And, the dosage of each material was consistent with the effect of the dosage of a single formula on the properties of adhesives. The performance of the color antiwearing thin layer was tested by the adhesion test and antiwearing durability test. It was found that temperature had a significant effect on the adhesion, the adhesion of the thin layer was significantly reduced at low temperature, and the sensitivity to impact load was enhanced, while the adhesion and sensitivity to impact load were effectively improved at more than 20°C. At the same time, the antiwearing of the thin layer decreased rapidly at the initial stage under the reciprocating load but tended to be stable when the load exceeds 500 times.

Complete unification in 10d E8

A grand unification scenario is presented that is based on quantum field theory, and where a single [Formula: see text] gauge superfield in 10 dimensions is used to obtain all the particle content of the Standard Model at low energies. The key feature of the formulation lies in the dimensional reduction used to break the gauge symmetry and to determine the low energy spectrum. It is shown that, through the orbifold [Formula: see text], and its corresponding Wilson lines, the symmetry is broken to the Standard Model one, generating a particular model that includes the Minimal Supersymmetric Standard Model spectrum. Furthermore it is also shown that the model is free of gauge anomalies at all levels by itself, i.e. without the need to include any additional representations of fields. Thus a complete unification of the Standard Model into a single gauge superfield is shown to be formally plausible. Although this paper does not include a phenomenological study of the specific model (currently being investigated), some interesting questions and observations are included as motivation for the scenario.

GAMMA RAY INDEX–SHALE VOLUME TRANSFORMS

Although a relationship between gamma ray log response and shale volume had been recognized since the introduction of gamma ray logging in the late 1930s and early 1940s, the formula for gamma ray index, and the equating of gamma ray index to shale volume apparently appeared in the late 1960s. Contemporaneously there appeared three similar, alternative, non-linear relationships in 1969, 1970, and 1971. These functions were based upon observations and empirical graphical functions. Subsequently, these graphical functions were fit using very dissimilar-looking formulas. Only the 1969 data set was published in support of the graphical functions. No attempt to link these functions with a single formula was ever made, and only vague verbal explanations have been offered for the non-linear functions. Further, the 1969 publication was in Russian, partly mistranslated, and the mistranslation never corrected. Consequently, two of the resulting formulas are misapplied. In this article I review the four standard non-linear functions (i.e., Larionov’s two, Stieber’s, Clavier’s), examine their similarities, and show that a single function would serve the same purpose as all four, thereby eliminating a source of confusion for formation evaluators. When these shale (or clay) volume versus gamma ray index transforms are inverted to functions of gamma ray index versus shale (or clay) fractional volume a remark-able property is revealed: the increment of radioactivity per unit shale volume decreases with increases in fractional shale volume. In other words, if one unit of shale per unit volume produces a gamma ray intensity of 10 API units we would think it strange if 10 units of shale per unit volume produced only, say, 60 API units of gamma radiation (instead of 100). Yet, this is the message contained in these functions. The cause for this phenomenon has been speculated upon, but only briefly and not often. To remedy this lack of speculation, I propose a physical model and give it mathematical form. This model is in-tended as a challenge to theoretical-minded petrophysicists to falsify it, make it better, or propose an alternative and more realistic model. I also provide (in Appendix C) a digital listing of all the published graphical data in the literature that support the introduction of the non-linear shale (and clay) fractional volume – gamma ray index transforms.