scholarly journals A general method of calculating the angles made by any planes of crystals, and the laws according to which they are formed

1833 ◽  
Vol 2 ◽  
pp. 227-229
Keyword(s):  
General Formula ◽  
Dihedral Angle ◽  
The Other ◽  
Plane Angle ◽  
General Process ◽  
Primitive Forms ◽  
Primary Form ◽  
General Method ◽  
Universal Application

The author, after stating the inconsistencies, inelegancies, and imperfections of the received notation for expressing the planes of a crystal, and the laws of decrement by which they arise, and of the usual methods of calculating their angles, explains the object of the present paper, which is to propose a system exempt from these inconveniencies, and adapted to reduce the mathematical portion of crystallography to a small number of simple formulae, of universal application. According to the method here followed, each plane of a crystal is represented by a symbol indicative of the laws from which it results, which, by varying only its indices, may be made to repre­sent any law whatever; and by means of these indices, and of the primary angles of the substance, we may derive a general formula expressing the dihedral angle contained between any one plane resulting from crystalline laws, and other . In the same manner we can find the angle contained between any two edges of the de­rived crystal. Conversely, having given the plane, or dihedral an­gles of any crystal, and its primary form, we can, by a direct and general process, deduce the laws of decrement according to which it is constituted. The purely mathematical part of this paper depends on two formulæ, demonstrated by the author elsewhere and here assumed as known; by means of one of which the dihedral angle included between any two planes can be calculated, when the equations of both planes are given; and by the other, the plane angle included between any two given right lines can in like manner be expressed by assigned functions of the coefficients of their equations, supposed given. These formulæ being taken for granted, nothing remains but to express by algebra­ical equations the planes which result from any assigned laws of decrement, for the different primitive forms which occur in crystallography.

scholarly journals IV. A general method of calculating the angles made by any planes of crystals, and the laws according to which they are formed

1825 ◽  
Vol 115 ◽  
pp. 87-130 ◽  
Keyword(s):  
General Formula ◽  
Dihedral Angle ◽  
General Expression ◽  
Dihedral Angles ◽  
General Process ◽  
Primary Form ◽  
General Method ◽  
Universal Application

1. It has been usual to calculate the angles of crystals and their laws of decrement from one another, by methods which were different as the figure was differently related to its nucleus; which were consequently incapable of any general expression or investigation, and which had no connexion with the notation by which the planes of the crystals were sometimes expressed. And the notation which has hitherto been employed, besides being merely a mode of registering the laws of decrement, without leading to any. consequences, is in itself very inelegant and imperfect. The different modes of decrement are expressed by means of different arbitrary symbols; and these are combined in a manner which in some cases, as for instance in that of intermediary decrements, is quite devoid both of simplicity and of uniformity, and indeed, it may be added, of precision. The object of the present paper is to propose a system which seems exempt from these inconveniences, and adapted to reduce the mathematical portion of crystallography to a small number of simple formulæ of universal application. According to the method here explained, each plane of a crystal is represented by a symbol indicative of the laws from which it results; the symbol, by varying the indices only, may be made to represent any law whatever: and by means of these indices, and of the primary angles of the substance, we obtain a general formula, expressing the dihedral angle contained between any one plane resulting from crystalline laws, and any other . In the same manner we can find the angle contained between any two edges of the derived crystal. Conversely, knowing the plane or dihedral angles of any crystal, and its primary form, we can by a direct and general process deduce the laws of decrement according to which it is constituted. The same formula are capable of being applied to the investigation of a great variety of properties of crystals of various kinds, as will be shown in the sequel. We shall begin with the consideration of the rhomboid, and the figures deduced from it; and we shall afterwards proceed to other primary forms.

scholarly journals The Dissociation of the Compound of Iodine and Thio-urea

1904 ◽  
Vol 24 ◽  
pp. 233-239 ◽  
Author(s):  
Hugh Marshall
Keyword(s):  
Nitric Acid ◽  
General Formula ◽  
Free Acid ◽  
The Other ◽  
Image Position

When thio-urea is treated with suitable oxidising agents in presence of acids, salts are formed corresponding to the general formula (CSN2H4)2X2:—Of these salts the di-nitrate is very sparingly soluble, and is precipitated on the addition of nitric acid or a nitrate to solutions of the other salts. The salts, as a class, are not very stable, and their solutions decompose, especially on warming, with formation of sulphur, thio-urea, cyanamide, and free acid. A corresponding decomposition results immediately on the addition of alkali, and this constitutes a very characteristic reaction for these salts.

Mastication of Rubber. II. Interpolymerization of Natural Rubber and Neoprene on Cold Milling

1956 ◽  
Vol 29 (2) ◽  
pp. 427-437
Author(s):  
D. J. Angier ◽  
W. F. Watson
Keyword(s):  
Free Radicals ◽  
Natural Rubber ◽  
Small Molecules ◽  
The Other ◽  
Polymer Molecules ◽  
Commercially Important ◽  
The Individual ◽  
Cold Mill ◽  
General Method ◽  
Butadiene Styrene

Abstract The softening of elastomers on cold milling results from scission of the polymer molecules by the applied shearing forces. The ruptured chains are free radicals, which can undergo mutual combination, interaction with oxygen and various additives, and branching (grafting) on to other polymer molecules. A general method of producing graft and block interpolymers between elstomers is therefore indicated, namely, to cold-mill the polymers together in the absence of small molecules which can terminate the polymeric radicals in order that the radicals may cross-terminate or graft onto the polymer molecules of the other type. A survey of several pairs of the commercially important elastomers, natural rubber, butadiene-styrene, Neoprene, and butadiene-acrylonitrile, has shown that cold milling does effect interlinking. Detailed results for the rubber-Neoprene system are reported in this communication. Experimental verification of polymer interlinking was obtained from the solubility properties of the milled elastomers. Cold milling of Neoprene under nitrogen produces gel, whereas of natural rubber does not, but the milling of mixtures gives gels containing natural rubber. Also, the solubilities and precipitation of the milled mixtures cannot be accounted for by these properties of the individual polymers. Finally, Neoprene-natural rubber mixtures, after and not before cold-milling, can be cross-linked by magnesium oxide, with rubber bound into the vulcanizate.

2,5-Bis(3,7-dichloroquinolin-8-yl)-1,3,4-oxadiazole

2006 ◽  
Vol 62 (7) ◽  
pp. o2594-o2595 ◽  
Author(s):  
E Ye ◽  
Yong-Wei Zhang ◽  
Hui Wang ◽  
Yun-Yin Niu ◽  
Seik Weng Ng
Keyword(s):  
Molecular Structure ◽  
Dihedral Angle ◽  
Triazole Ring ◽  
The Other ◽  
Central Ring ◽  
Steric Crowding

In the title molecular structure, C20H8Cl4N4O, the 1,3,4-triazole ring is twisted with an r.m.s. deviation of 0.0035 Å. One of the quinolinyl substituents makes a dihedral angle of 55.8 (1)° with respect to the central ring, while the other is rotated by 71.7 (1)°; these twists are necessary to relieve steric crowding.

scholarly journals Crystal structure of 4-({5-[(E)-(3,5-difluorophenyl)diazenyl]-2-hydroxybenzylidene}amino)-2,2,6,6-tetramethylpiperidin-1-oxyl

2015 ◽  
Vol 71 (7) ◽  
pp. 864-866
Author(s):  
Ramazan Tatsız ◽  
Veli T. Kasumov ◽  
Tuncay Tunc ◽  
Tuncer Hökelek
Keyword(s):  
Dihedral Angle ◽  
Three Dimensional ◽  
Chair Conformation ◽  
The Other ◽  
Supramolecular Network ◽  
Stacking Interactions ◽  
Asymmetric Unit ◽  
Compound C ◽  
Benzene Rings ◽  
Independent Molecules

The asymmetric unit of the title compound, C22H25F2N4O2, contains two crystallographically independent molecules. In one molecule, the two benzene rings are oriented at a dihedral angle of 1.93 (10)° and in the other molecule the corresponding dihedral angle is 7.19 (9)°. The piperidine rings in the two molecules adopt a similar distorted chair conformation, and both have pseudo-mirror planes passing through the N—O bonds. An intramolecular O—H...N hydrogen bond between the hydroxy group and the imine N atom is observed in both molecules. In the crystal, weak C—H...O and C—H...F hydrogen bonds, enclosingR22(6) ring motifs, and weak π–π stacking interactions link the molecules into a three-dimensional supramolecular network, with centroid-to-centroid distances between the nearly parallel phenyl and benzene rings of adjacent molecules of 3.975 (2) and 3.782 (2) Å.

Robust Passive-Active Mounts for Machinery and Equipment

1997 ◽  
Author(s):  
J. Hannsen Su
Keyword(s):  
Resonant Frequency ◽  
Vibration Isolation ◽  
Vibration Suppression ◽  
Low Frequency ◽  
The Other ◽  
Resonant Frequencies ◽  
Vibration Magnitude ◽  
Fixed End ◽  
Degradation Problem ◽  
Universal Application

Abstract Conventional vibration isolation mounts are not as effective as expected on a practical foundation whose resonant frequencies normally are within the bandwidth of interest. In addition, the low frequency enhancement is a characteristic of the passive mounts. Applying inertia actuators to the bottom attachment plate of the conventional mounts overcomes these shortcomings and enhances their performance significantly. This design concept has universal application since it is applicable to any dynamic system. It requires very little power and force capacity, i.e., a small percentage of the disturbance force, from the actuators to be effective for frequencies higher than the resonant frequency of the mount itself. The effectiveness of the proposed mounts for the machinery is demonstrated on the load transmissibility reduction at the foundation support (fixed end) due to disturbance from machinery above mounts. On the other hand, the vibration magnitude reduction of equipment above mounts due to disturbance from the foundation is used for evaluating the equipment isolation effectiveness. There is no stabilty or degradation problem when a number of the passive-active mounts are used on the same foundation. Furthermore, the more of this type of mounts used on a foundation the more effective the vibration suppression and the smaller actuator force requirement for each passive-active mount.

Now you see it, now you don’t: Design dependent sound symbolism effect in categorization studies

2012 ◽  
Vol 25 (0) ◽  
pp. 65 ◽  
Author(s):  
Vanja Kovic ◽  
Jovana Pejovic
Keyword(s):  
Mental Image ◽  
Visual Stimuli ◽  
Sound Symbolism ◽  
The Other ◽  
Visual Features ◽  
General Process ◽  
Visual Objects ◽  
The One ◽  
Label Object ◽  
Is Design

A number of studies have demonstrated sound-symbolism effects in adults and in children. Moreover, recently, ERP studies have shown that the sensitivity to sound-symbolic label–object associations occurs within 200 ms of object presentation (Kovic et al., 2010). It was argued that this effect may reflect a more general process of auditory–visual feature integration where properties of auditory stimuli facilitate a mapping to specific visual features. Here we demonstrate that the sound-symbolism effect is design dependent, namely — it occurs only when mapping from auditory to visual stimuli and not vice verse. Two groups of participants were recruited for solving the categorization task. They were presented them with 12 visual stimuli, half of which were rounded and another half of angular shapes. One group was trained to classify the rounded objects as ‘takete’ and the rounded ones as ‘maluma’, whereas the other group mapped ‘takete’ to rounded and ‘maluma’ to angular shapes. Moreover, half of these two groups heard the label before seeing the objects, whereas the other half was given the label after perceiving the object. The results revealed the sound-symbolism effect only in the group which was trained on the auditory–visual objects mapping and not in the one trained on the visual–auditory mappings. Thus, despite the previous findings we demonstrate that the sound-symbolism effect is not significant per se, but design-dependent and we argue that the sound brings up a mental image that is more constrained than the sounds brought up by a picture.

Paraconsistency, self-extensionality, modality

2018 ◽  
Vol 28 (5) ◽  
pp. 851-880
Author(s):  
Arnon Avron ◽  
Anna Zamansky
Keyword(s):  
Intuitionistic Logic ◽  
Modal Logics ◽  
The Other ◽  
Paraconsistent Logics ◽  
Classical Negation ◽  
Inconsistent Theories ◽  
Replacement Property ◽  
General Method

Abstract Paraconsistent logics are logics that, in contrast to classical and intuitionistic logic, do not trivialize inconsistent theories. In this paper we take a paraconsistent view on two famous modal logics: B and S5. We use for this a well-known general method for turning modal logics to paraconsistent logics by defining a new (paraconsistent) negation as $\neg \varphi =_{Def} \sim \Box \varphi$ (where $\sim$ is the classical negation). We show that while that makes both B and S5 members of the well-studied family of paraconsistent C-systems, they differ from most other C-systems in having the important replacement property (which means that equivalence of formulas implies their congruence). We further show that B is a very robust C-system in the sense that almost any axiom which has been considered in the context of C-systems is either already a theorem of B or its addition to B leads to a logic that is no longer paraconsistent. There is exactly one notable exception, and the result of adding this exception to B leads to the other logic studied here, S5.

scholarly journals Quantum key distribution with correlated sources

2020 ◽  
Vol 6 (37) ◽  
pp. eaaz4487 ◽  
Author(s):  
Margarida Pereira ◽  
Go Kato ◽  
Akihiro Mizutani ◽  
Marcos Curty ◽  
Kiyoshi Tamaki
Keyword(s):  
Quantum Key Distribution ◽  
Key Distribution ◽  
The Other ◽  
Correlated Sources ◽  
Information Theoretic ◽  
Security Proofs ◽  
Information Theoretic Security ◽  
Special Cases ◽  
New Framework ◽  
General Method

In theory, quantum key distribution (QKD) offers information-theoretic security. In practice, however, it does not due to the discrepancies between the assumptions used in the security proofs and the behavior of the real apparatuses. Recent years have witnessed a tremendous effort to fill the gap, but the treatment of correlations among pulses has remained a major elusive problem. Here, we close this gap by introducing a simple yet general method to prove the security of QKD with arbitrarily long-range pulse correlations. Our method is compatible with those security proofs that accommodate all the other typical device imperfections, thus paving the way toward achieving implementation security in QKD with arbitrary flawed devices. Moreover, we introduce a new framework for security proofs, which we call the reference technique. This framework includes existing security proofs as special cases, and it can be widely applied to a number of QKD protocols.

A New General Method for the Determination of Optical Properties of Amorphous Silicon Films

1990 ◽  
Vol 192 ◽  
Author(s):  
G. Amato ◽  
L. Boarino ◽  
F. Fizzotti ◽  
C. Manfredotti
Keyword(s):  
Thin Films ◽  
Optical Properties ◽  
Amorphous Silicon ◽  
Optical Response ◽  
The Other ◽  
New Method ◽  
Silicon Thin Films ◽  
Physical Insight ◽  
General Method

ABSTRACTWe propose to apply a new method to model the optical response of amorphous silicon thin films. This method presents the advantage of having a good physical insight. On the other hand, although the model has been originally tested on different materials like a-Si, a-Ge and a-GaAs, we show that it is also sensitive to small differences like those that can exist between intrinsic and doped a-Si:H.

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