Left-handed Members Research Articles

Curve-Surface Pairs on Embedded Surfaces and Involute D-Scroll of the Curve-Surface Pair in E3

Willmore defined embedded surfaces on f:S→E3, which is the embedding of S into Euclidean 3-space. He investigated the Euclidean metric of E3, inducing a Riemannian structure on f(S). The expression analogous to the left-hand member of the curvature K is replaced by the mean curvature H2 on f(S). Our aim is to observe the Gaussian and mean curvatures of curve–surface pairs using embedded surfaces in different curve–surface pairs and to define some developable operations on their curve–surface pairs. We also investigate the embedded surfaces using the Willmore method. We first recall the Darboux curve–surface and derive the new characterizations. This curve–surface pair is called the osculating Darboux curve–surface if its position vector always lies in the osculating Darboux plane spanned by a Darboux frame. Thus, we observed an osculating Darboux curve–surface pair. We also obtained the D∼-scroll of the curve–surface pair and involute D∼-scroll of the curve–surface pair with some differential geometric elements and found D∼(α,M)(s) and D∗∼(α,M)(s)-scrolls of the curve–surface pair (α,M).

Compound-Internal Language Mixing in American Norwegian

This paper investigates cases of compounding in the heritage language American Norwegian (AmNo), where elements from Norwegian and English are mixed word-internally, e.g., hoste-candy ‘cough candy’, where the Norwegian item hoste ‘cough’ is combined with the English item candy. Norwegian and English create compounds in similar ways, but with certain important differences, e.g., the use of linking elements. Based on data from the Corpus of American Nordic Speech, we investigate the encounter of these two languages within one word and find that both Norwegian and English lexical items occur as both left-hand and right-hand members of mixed compounds. Moreover, these mixed compounds are generally accompanied by Norwegian functional items. Hence, we argue that the overall structure of mixed compounds in AmNo is Norwegian, and English lexical items may be inserted into specific positions. This is successfully analyzed in a DM/exoskeletal model of grammar. We show that our results are in line with what we expect based on previous accounts of AmNo language mixing and Norwegian compounds, and our specific focus on compound-internal mixing provides a novel perspective and new insights into both the structure of compounds and the nature of language mixing.

DEVELOPMENT OF WOOD GRINDING. 3. FURTHER TESTING OF GRINDING MODELS

"The study is the continuation of a sequence of works devoted to describing the mechanisms occurring during stone grinding of wood. This part was aimed at further testing of pressurised grinding of spruce wood, which was conducted under controlled laboratory conditions. Testing of the developed theoretical model for power ratio (Pc/Pt) versus energy specific production (Ġw/Pt) produced linears for data representing constant wood moisture content. However, the linears showed almost identical results for fresh woods, and also for drier wood, e.g. wood containing saturated fibres and air-dried wood, although one would expect some differences due to the widely varying constant moisture, from 65% to 15% moisture content. Simplification of the model resulted in (cw + X cm) ΔTp-w ≈ Pt / Ġw, and it led to specific linears, when the members as such were correlated between themselves at several constant wood moisture contents. The results were briefly as follows. Increasing wood feed rate – 0.7, 1.0 and 1.3 mm/s – decreased the specific energy requirement, while increased stone surface speed – 20 and 30 m/s – increased it. The left-hand member or the “X-factor” as named in this context, correlated with the right-hand member or the specific energy requirement and resulted in declining linears. The lower the wood moisture content – 65, 58, 44, 28 and 15% – the smaller was the linear declination, and also the difference due to stone surface speed. The application of an energy balance could be useful in searching for a working wood grinding model. Such a model would enable critical examination of wood grinding conditions. Also, it would help understanding the mechanism of various factors, such as grinding parameters, wood properties and stone burr and sharpness. It seems that there are factors that are not known well enough for further development of grinding. Shower water flow and temperature affect the stone surface temperature as known, but their significance for the energy balance or grinding mechanism are not known. Also, the thin film of pulp slurry between the stone surface and the heat activated wood layer is evidently a significant factor that is connected to the local energy transfer. "

Extravagant “fake” morphemes in Dutch. Morphological productivity, semantic profiles and categorical flexibility

AbstractDutch features several morphemes with “privative” semantics that occur as left-hand members in compounds (e.g.,imitatieleer‘imitation leather’,kunstgras‘artificial grass’,nepjuwelen‘fake jewels’). Some of these “fake” morphemes display great categorical flexibility and innovative adjectival uses.Nep, for instance, is synchronically attested as an inflected adjective (e.g.,neppe cupcake‘fake cupcake’). In this paper, we combine an extensive corpus study of eight Dutch “fake” morphemes with statistical methods in distributional semantics and collexeme analysis in order to compare their semantic and morphological properties and to find out which factors are the driving forces behind their exceptional “extravagant” morphological behavior. Our analyses show that debonding and adjectival reanalysis are triggered by an interplay of two factors, i.e., type frequency and semantic coherence, which allow us to range the eight morphemes on a cline from more schematic to more substantive “fake” constructions.

Dark Experiments: From Black Holes to Cosmic Rays

Some nagging questions in modern physics can be resolved rigorously using a basic mathematical formalism, albeit with the need to admit that non-isomorphic realities arise to various degrees in a given universe. Let U=(m', m) be an unordered pair of distinct massive objects in different reference frames. A dark experiment is an ordering u, mv> of the elements of U, either or, exclusively, , where the left-hand member of the ordered pair is called the observer, and where there exists a 1-to-1 mapping f:{u}→{events}, mv> , such that both elements of an ordered pair in a dark experiment agree on the events that unfold in the experiment. However, since ≠ , it follows that f()≠f(). This describes non-isomorphic realities where in both elements of each ordered pair mapping two distinct sets of unfolding events will agree on their respective events. Consequently, there is an inherent limitation on what can be determined directly from experimentation. Examples arise in the context of the Hawking information paradox, relativistic time travel, and cosmic ray experiments.

Van boekenbonnen en feëverhale - De tussenklank e(n) in Nederlandse en Afrikaanse samenstellingen: vorm of betekenis?

Compounds in Dutch and Afrikaans may contain a linking sound resembling the plural suffix [ə] or [ən]. This linking sound can be spelled in Dutch as e or en, a difference which previous research has shown to affect the interpretation of left hand members of compounds regarding their plurality. Here, we look at the existence of the reverse effect: do semantic clues about number influence preferences for a linking sound in novel compounds? Indeed, contexts in which the left hand member of a compound-to-be is present in its plural form increase the tendency to prefer a linking element (using a seven-point rating scale). In contexts which merely suggest a plural interpretation for the left hand member, this propensity is markedly less for speakers of Dutch, and absent for speakers of Afrikaans. Of interest is the asymmetry with previous research that shows how subtle form differences influence number interpretation.

The Role of Semantics, Argument Structure, and Lexicalization in Compound Stress Assignment in English

It is generally assumed that noun-noun compounds in English are stressed on the left-hand member (e.g. cóurtroom wátchmaker ). However, there is a large amount of variation in stress assignment (e.g. silk tíe, Madison Ávenue, singer-sóngwriter ) whose significance and sources are largely unaccounted for in the literature. This article presents a study in which three kinds of factors held to play a role in compound stress assignment are tested: argument structure, lexicalization, and semantics. The analysis of 4,353 noun-noun compounds extracted from the Boston University Radio Speech Corpus shows that there is indeed a considerable amount of variation in stress assignment. Overall, semantics turns out to have the strongest effect on compound stress assignment, whereas an approach relying on argument structure is much less successful in predicting compound stress. The article presents for the first time large-scale empirical evidence for the assumption that lexicalization has an effect on compound stress assignment. The article also makes a methodological contribution to the debate in showing that (and how) corpus-based studies using acoustic measurements can shed new light on the issue of variable compound stress.*

The variability of compound stress in English: structural, semantic, and analogical factors

It is generally assumed that noun–noun (NN) compounds in English are stressed on the left-hand member (e.g. cóurtroom, wátchmaker). However, there is a considerable amount of variation in stress assignment (e.g. silk tíe, Madison Ávenue, singer-sóngwriter), whose significance and sources are largely unaccounted for in the literature. This article presents an experimental study in which three competing hypotheses concerning NN stress assignment are tested. The stress patterns of novel and existing compounds, as obtained in a reading experiment with native speakers of American English, were acoustically measured and analyzed. The results show that there is indeed a considerable amount of variation in stress assignment, and that all three hypothesized factors, i.e. structure, semantics, and analogy, are relevant, though to different degrees. On a theoretical level, the findings strongly suggest that a categorical approach cannot be upheld and that probability and analogy need to be incorporated into an adequate account of stress assignment in noun–noun constructions. The article also makes a methodological contribution to the debate in showing that experimental studies using pitch measurements can shed new light on the issue of variable compound stress.

Continuation theorems for periodic perturbations of autonomous systems

It is first shown in this paper that, whenever it exists, the coincidence degree of the left-hand member of an autonomous differential equation \[ x’ - {\text {g}}(x) = 0\], in the space of periodic functions with fixed period $\omega$, can be computed in terms of the Brouwer degree of ${\text {g}}$. This result provides efficient continuation theorems specially for $\omega$-periodic perturbations of autonomous systems. Extensions to differential equations in flow-invariant ENR’s are also given.

Continuation Theorems for Periodic Perturbations of Autonomous Systems

It is first shown in this paper that, whenever it exists, the coincidence degree of the left-hand member of an autonomous differential equation \[ x’ - {\text {g}}(x) = 0\], in the space of periodic functions with fixed period $\omega$, can be computed in terms of the Brouwer degree of ${\text {g}}$. This result provides efficient continuation theorems specially for $\omega$-periodic perturbations of autonomous systems. Extensions to differential equations in flow-invariant ENR’s are also given.

Handedness patterns in deaf persons

The handedness patterns of 226 deaf high-school and college students were compared to those of 210 college students with normal hearing. Both groups evidenced many more right-handed than left-handed members, as determined by responses to a hand preference questionnaire and performance on an activity test battery. There was, however, a significantly higher incidence of left-handedness among the deaf subjects than among the hearing. Moreover, the left-handed deaf students were found to be less likely to have deaf relatives, and to have been introduced to sign language later in their development than the deaf student population as a whole. These findings were interpreted as showing that age of acquisition of language was related to the development of handedness patterns, whereas auditory processing experience probably was not.

Acoustic similarity effects on long-term memory for paired associates

Does acoustic similarity between the left-hand members of two paired-associate (PA) lists impair long-term memory (LTM) in a proaction design? Under one treatment, the left-hand terms of the two lists were acoustically similar (e.g., YOUNG-LUNG); under a second treatment, they were not acoustically similar. Either 10 min, 24 hr, or 1 week intervened between the end of List 2 learning and the recall test on List 2. Subsequent to the memory test on List 2, retention of List 1 was also assessed. Neither recall of List 2 nor memory for List 1 was substantially affected by the manipulation in acoustic similarity. For LTM following multitrial training on two full-scale PA lists, it is concluded that both proactive and retroactive inhibition attributable to acoustic similarity between the left-hand terms of the lists are negligible.

Acoustic similarity effects on memory for paired associates

Experiment I tested the short-term retention of paired associates (PAs) with 6-item PA lists and a probe technique. Acoustic similarity between the left-hand members (e.g., LAMPRAMP) of specific pairs increased proactive inhibition but not retroactive inhibition (RI). Experiment II, which used the same kind of materials, examined RI in memory for PAs following multi-trial practice on two consecutive PA lists. Acoustic similarity had no substantial effect on retention of the first list or learning of the second list. These data suggest that, in short-term retention at least, acoustic similarity effects on the memory for PAs are mostly proactive.

Figural equivalence in the white rat

In experiments on figural-discrimination learning, monkeys, cats and pigeons can transfer their acquired responses to the relevant stimuli even when the figure-ground brightness is reversed. Transfer is, however, interfered with in rats. This experiment is concerned with the nature of figural discrimination in white rats, especially when the figure-ground relationship and stimulus, patterning are changed.Subjects : Eight experimentally naive white male rats.Apparatus: Lashley' s jumping stand painted black.Stimulus cards : The training cards consisted of a white triangle apex down (positive) and a white circle (negative) on a black ground (Fig. 1). Test cards for equivalence are shown in Fig. 252.Procedure : After one week's preliminary training, ten discrimination learning trials were run per day until the rats reached the criterion of 19 successively correct trials out of 20. After reaching the criterion, rats were tested for equivalence responses with Fig. 252. In this period, each animal received ten training and 20 test trials per day, successively. Each rat was tested with each of the 51 pairs of test figures.Results : Table 1 shows total number of trials required to reach the criterion, and Table 2 to Table 13 (inclusive) the percent of the responses to the left-hand member of the pair of Fig. 252. Criterion of equivalence is 80 percent. Numerals in parentheses at the side of each figure represent numbers of rats reached criterion eight in all.Conclusions : Several conclusions are indicated by the data.(1) Reversal of absolute figure-ground brightness disrupts discrimination.However, when the relative brightness of figure-ground are maintained, equivalent responses can be seen.(2) Transfer was shown to the incomplete figures and outlines, and the dominant feature of the responses depends chiefly on the lower part of figures.(3) The original discriminatory response had its basis in an adient response to the triangle, as well as in avoidance of the negative circle.(4) The disposition to respond to a familiar figure, even to originally negative circle, was increased when one of the original pair was substituted with a stimulus not previously used.It was discussed that the nature of the equivalence in the figural discrimination by the rat depends on stimulus patterning including figure-ground relationships.

On functions holomorphic in a strip region, and an extension of Watson’s problem

In the usual statement of this theorem, for example Ostrowski [9, pp. 195— 196](2), it is supposed that <p(C) is holomorphic on ^(f) =0. If we note, however, that if f(x) ??0 is holomorphic and bounded in |a;| <1, and continuous on |jc| =1 except perhaps at x = l, then the set of points on |ac| =1 where f(x) =0 is of measure zero(3), it is evident that a slight modification of Ostrowski's proof yields Theorem A(4). Since 0(f) is bounded, (1) is equivalent to stating that the left-hand member of (1) is finite. Conversely there follows from well known results:

On the Approximate Solutions in Integers of a Set of Linear Equations

where ai, . .., an, , ..., ,n are 2n given real numbers, the first n of which are subject to a condition (C) stated below. The degree of approximation is as follows: having specified a positive number e as small as we please, then the numerical values of the left-hand members of the above equations (i.e., the "errors") can simultaneously be made smaller than e. The condition (C) imposed upon al, a2, .... an is this: they are to be irrational numbers of such a nature that a linear expression of the form aO + alai + ... + a,,a,,, with integral coefficients a, a, ..., a,,, can vanish exactly only when these coefficients are all = 0. For a given approximate solution of the equations (1) the errors shall be designated, respectively, by El, ..., Ce. 2. In the two special cases: (I) n = 1, or (II) 13 =2 = ... O= /n = 0, we can make additional demands upon the errors, namely (and this is of importance in applications) we can cause them to be smaller than certain corresponding functions of w. Thus, in the case (I), we can demand that ei < e and at the same time that e < 1/(4 1 w 1); in case (II) we can demand that Ei, ..., en be each < e and at the same time < k/( I w )', where k = n/(n + 1), and m = -(n 1)/n; furthermore, the condition (C) is not necessary in case (II).3 These results may be stated in another way: in case (I), a being irrational, an infinite number of sets of integers (x', w'), (x", w"), .... exist which, when substituted in turn in x aw , = 0, will produce errors e', e", .... of such magnitudes that e' < 1/(41 w' |), |" < 1/(41 w" |), etc. Similarly, in case (II) we have an infinite number of solutions satisfying corresponding inequalities. 3. In the general case the errors cannot be made to satisfy such extra demands. Stated more precisely: no matter what function f(w) be assumed, if only it be subjected to the conditions (D) below, we can always construct a set of equations (1) with attendant condition (C), which do not admit an infinite number of approximate solutions in integers (x1, x2, . .. , X,,), ...., if we demand the following degree of accuracy for each solution: e1 < f( | w | ), ..., E,, < f( w | ). In fact, we may even substitute the weaker demand.

On The Variation of the FactorhIn The Equation12mv2=hν

Relation between the $\ensuremath{\beta}$- and $\ensuremath{\gamma}$-rays of Ra B; Theory.---The author has previously shown that by combining the equations for orbital motion of an electron about a central positive charge with the equation $\frac{1}{2}m{v}^{2}=h\ensuremath{\nu}$, the magnitude of the central positive charge about which a radiating electron is revolving may be calculated, and that when this value of the central charge is equated with one derived from an equation of the form of Moseley's equation for the frequency of X-rays the wave-length of the shortest lines in the K-radiation of elements of atomic numbers from 35 to 58 may be calculated as accurately as they can be measured. Later measurements of wave-lengths of elements with higher atomic numbers show that the computed wave-lengt hs vary progressively from the measured wave-lengths as the atomic numbers increase. It is also known that Moseley's law for the frequency of X-rays varies in the same manner.The equation from which the author calculates the wave-length is $\frac{{2}^{\frac{1}{2}}{h}^{\frac{3}{2}}{c}^{\frac{1}{2}}}{{m}^{\frac{1}{2}}{\ensuremath{\lambda}}^{\frac{1}{2}}e\ensuremath{\pi}}=2e(N\ensuremath{-}3.6).$Since the right-hand member of this equation shows that the nuclear charge in the case of K-radiation increases by $2e$ in passing from one element to the one of next higher atomic number, it is not probable that this law breaks down at atomic number 58, and that the nuclear charges of elements of higher atomic number increase by variable quantities. The failure of the equation to apply to elements of higher atomic number must then be looked for in the left-hand member. In this member the only variable quantities (since $\ensuremath{\lambda}$ is measured) are $m$, the mass of the electron, and possibly $h$, the Einstein factor. These quantities appear in the form of the ratio $\frac{{h}^{3}}{m}$, and the author has calculated values of $\frac{{h}^{3}}{m}$ which substituted in his equation will give the correct wave-lengths for elements of higher atomic number. These values of $\frac{{h}^{3}}{m}$ are then plotted against their corresponding wave-lengths and a smooth curve is obtained. Values of $\frac{{h}^{3}}{m}$ are then taken from this curve for a number of the $\ensuremath{\gamma}$-ray wave-lengths measured by Rutherford and Andrade. These wave-lengths are then assigned to certain groups of $\ensuremath{\beta}$-rays from Radium B on grounds which seem to the author permissible. The mass, $m$, and the quantity $h$ corresponding to the speeds of these $\ensuremath{\beta}$ particles were then computed. The values of $h$ computed in this way seem to be derivable from $m$ by the equation $h=4.25 logm+2.50\ifmmode\cdot\else\textperiodcentered\fi{}{10}^{\ensuremath{-}27}$. Using this value of $h$, wave-lengths were computed for the fourteen groups of $\ensuremath{\beta}$-rays from Radium B whose speeds were measured by Rutherford, and nine of them were found to agree satisfactorily with wave-lengths in the $\ensuremath{\gamma}$-radiation of Radium B and Radium C, while two more of the measured wave-lengths seem to correspond with the speeds of $\ensuremath{\beta}$-particles from Radium C.Calculation of Orbital Velocities of Radiating Electrons by Substituting $4.25 \mathrm{log} m+2.50\ifmmode\cdot\else\textperiodcentered\fi{}{10}^{\ensuremath{-}27}$ for $h$ in the equation $\frac{1}{2}m{v}^{2}=h\ensuremath{\nu}$.Using a series of values of $v$ from 0.1\ifmmode\cdot\else\textperiodcentered\fi{}${10}^{10}$ to 2.2\ifmmode\cdot\else\textperiodcentered\fi{}${10}^{10}$ corresponding values of $m$ were calculated from Bucherer's equation for the transverse mass of an electron, viz., $m=\frac{{m}_{0}}{\sqrt{\mathrm{I}\ensuremath{-}\frac{{v}^{2}}{{c}^{2}}}}$. From these values $\ensuremath{\nu}$ was computed using the equation $\ensuremath{\nu}=\frac{\frac{1}{2}m{v}^{2}}{(4.25 logm+2.50)}$, and these values of $\ensuremath{\nu}$ were plotted on a large scale as abscissas using the values of $v$ from which they were derived as ordinates. From this curve were taken values of $v$ corresponding to all the highest frequencies of K-radiation as measured by Siegbahn and his colleagues and Duane and his colleagues. The values of $v$ obtained in this way are then compared with values calculated from the equation $v=2.054(N\ensuremath{-}\mathrm{I}.66)$ and are found to agree satisfactorily with no tendency to vary progressively with the higher numbers, as do the values calculated by Duane using $h$ as a constant.It is concluded that since $h$ may be replaced in the equation $\frac{1}{2}m{v}^{2}=h\ensuremath{\nu}$ by a function of $m$ with a great improvement in the accuracy of the equation, there is no longer ground for speaking of an energy quantum in this equation.

Algebraic properties of self-adjoint systems

The general definition of adjoint systems of boundary conditions associated with ordinary linear differential equations was given by Birkhoff.t In a paper of Bocher, I in which the idea is further developed, there is obtained a condition that a system of the second order be self-adjoint. It is proposed here to extend the discussion of this problem to the case of systems of any order.? A condition for self-adjointness of the boundary conditions is simply expressed in matrix form, without any requirement that a corresponding propertv be possessed by the differential equations; the condition gains in symmetry if it is assumed that the differential expression which forms the lefthand member of the given differential equation is itself identical with its adjoint or with the negative of its adjoint. As a preliminary, it will be well to recall a well-known rule for the combination of matrices, which will be found particuilarly convenient. Let a,, cx2, a3, and a4 be n-rowed square matrices. The square matrix of order 2n which is made up of the elements of these four, with the elements of al, arranged in order, in its upper left-hand corner, and the elements of the other matrices correspondingly disposed, may be indicated by the notation

I.—Elimination in the case of Equality of Fractions whose Numerators and Denominators are Linear Functions of the Variables.

(1) It is well known that if equations of the type referred to in the title be dealt with like ordinary quadrics, the eliminant obtained is marred by association with an irrelevant factor. Thus, to take the simplest case, viz.the left-hand member of which contains the irrelevant factor |α2β2|, being readily shown to be equal toThe object of the present short paper is to draw attention to other modes of procedure, and to formulate the results for n variables.

XIV. The relation between electric energy and radiation in the spectrum of incandescence lamps

In the “Philosophical Magazine” for September, 1883, we showed that certain relations existed between potential, current, watts (volt-ampères), and radiation in incandescence lamps, and that if p = the potential, c = current, w = watts, R = radiation, and a and b were constants, then (i) c = ap + bp 3/2 , and consequently that (ii) w = p 2 ( a + bp ½ ) ; further we showed that after the carbon filaments attained a certain heat, the radiation varied directly as the energy. (iii) R∝ ( w — m ) where m is a constant. We may incidentally mention that this relationship appears to hold good in a properly exhausted lamp, be the filament of carbon or of platinum, or presumably of other metals. In this case the sign in the left hand members of equations (i) and (ii) is changed. On laying down graphically the curve obtained by using the watts as the abscissæ and the radiation as ordinates, it was at once evident that the straight part is an asymptote to a curve having its origin at 0. It might, therefore, be presumed that each individual ray should increase in intensity in somewhat the same manner when the energy in the filament was increased, i. e. , in some simple curve which would have an asymptote.