• The Pure and Applied Mathematics
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• v.8 no.2
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• pp.127-135
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• 2001

The main object of this paper is to present a transformation formula for a finite series involving $_3F_2$ and some identities associated with the binomial coefficients by making use of the theory of Legendre polynomials $P_{n}$(x) and some summation theorems for hypergeometric functions $_pF_q$. Some integral formulas are also considered.

• Current Optics and Photonics
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• v.5 no.2
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• pp.180-185
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• 2021

A femtosecond-laser inscribed Yb:YAG surface channel waveguide (WG) laser with single-walled carbon nanotubes deposited on the top surface of the WG was passively Q-switched by evanescent field interaction. Q-switched operation of the 14-mm-long compact Yb:YAG WG laser was achieved near 1031 nm with two different pumping schemes (single- and double-pass pumping) with an output coupling transmission of 91%. The Q-switched pulse characteristics depending on the absorbed pump power were investigated for both pumping geometries and analyzed in detail based on theoretical modeling. The best performances (energy/pulse duration) for each configuration were 204.4 nJ/75 ns at a repetition rate of 1.87 MHz, and 201.1 nJ/81 ns at 1.75 MHz for single- and double-pass pumping, respectively.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.2
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• pp.74.1-74.1
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• 2019

We present the distance measurements of two spiral galaxies NGC 4517, NGC 4592, and neighboring dwarf galaxies found in Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) wide field survey data. Distances to NGC 4517 and NGC 4592 are measured by the Tip of the Red Giant Branch method from archival Hubble Space Telescope data; 9.00^+0.094_-0.260 Mpc for NGC 4517 and 8.90^+0.256_-0.060 Mpc for NGC 4592. The spatial distance between NGC 4517 and NGC 4592 is 300 kpc, which is close enough for them to be considered as a group (NGC 4517 group). Using resolved stellar photometry and Surface Brightness Fluctuation (SBF) method with HSC-SSP data, we estimate the distances to three other dwarf galaxies and confirm that they are members of the group. Velocities of three of the galaxies in the NGC 4517 group show that this group is one of the galaxy groups in the near side of the Virgo Cluster infall region.

• The Bulletin of The Korean Astronomical Society
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• v.45 no.1
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• pp.32.1-32.1
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• 2020

An independent determination of H0 is crucial given the growing tension of the Hubble constant (H0). In this work, we present a new determination of H0 using velocities and Tip of the Red Giant Branch (TRGB) distances to 33 galaxies in front of the Virgo Cluster. We model the infall pattern of the local Hubble flow modified by the Virgo mass, as a function of the H0, the radius of the zero-velocity surface R0, and the intrinsic velocity scatter. Fitting velocities and TRGB distances of 33 galaxies to the model, we obtain H0 = 65.6 +/- 3.4 (stat) +/- 1.0 (sys) km/s/Mpc and R0 = 6.96 +/- 0.35 Mpc. Our local H0 is consistent with the global H0 determined from cosmic microwave background radiation, showing no tension.

• Journal of Korean Philosophical Society
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• no.114
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• pp.177-212
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• 2016

Kants Begriff der Freiheit des Willens ist sehr kompliziert und verwirrend. Denn sowie es Ziel der ${\gg}$Kritik der praktischen Vernunft${\ll}$ ist, die reine praktische Vernunft zu beweisen, liegt der Fokus von Kants Begriff der Freiheit auf der Freiheit von Zwang, wobei Kant eine unbestimmte Haltung zur Freiheit von Notwendigkeit einnimmt und sie dann $schie{\ss}lich$ leugnet. Leibnizens Begriff der Freiheit dagegen hebt die Freiheit von Notwendigkeit hervor, denn er sagt, dass der menschliche Wille nicht nur vom Zwang der Leidenschaft, sondern auch von Notwendigkeit frei sei. Die Struktur von Leibnizens Freiheitslehre unterscheidet sich zwar sehr von der Kants, aber die Charakterlehren beider Denker, in denen die $M{\ddot{o}}glichkeit$ der Vereinbarkeit von Freiheit und Notwendigkeit behandelt werden, weisen viele Parallelen auf. Zudem ist Leibnizens Begriff der Freiheit sehr eindeutig. Daher ist ein Vergleich von Leibnizens und Kants Begriff der Freiheit nicht nur sinnvoll und $f{\ddot{u}}hrt$ zu einem besserem $Verst{\ddot{a}}ndnis$ von Kants Freiheitsbegriff, durch die vergleichende Analyse stellt sich zudem auch heraus, dass auch bei Kant nicht nur Freiheit von Zwang, sondern auch Freiheit von Notwendigkeit $m{\ddot{o}}glich$ ist. Leibniz geht $f{\ddot{u}}r$ seine Freiheitslehre von dem Begriff der Freiheit vom Zwang der Leidenschaft, welcher von allen Rationalisten anerkannt wird, sowie von dem Begriff der Freiheit von der Notwendigkeit, welcher von Spinoza negiert wird, aus. Kant dagegen definiert Freiheit als $Unabh{\ddot{a}}ngigkeit$ von den Naturgesetzen, was diesen Begriff von Anfang an unklar macht. Kant war sich anfangs der Zweideutigkeit dieses Konzepts nicht $bewu{\ss}t$ und hat es undeutlich gebraucht, doch in der Neuauflage von ${\gg}$Die Religion innerhalb der $blo{\ss}en$ Vernunft${\ll}$ erkennt er den Unterschied in den zwei Begriffen der Willensfreiheit, weshalb er bei der Rechtslehre in der ${\gg}$Metaphysik der Sitten${\ll}$ dazu kommt, die Wahlfreiheit zu negieren. Aber in den Abschnitten, wo Kant in der ${\gg}$Kritik der reinen Vernunft${\ll}$ und der ${\gg}$Kritik der praktischen Vernunft${\ll}$ die Vereinbarkeit von Freiheit und Notwendigkeit behandelt, $f{\ddot{u}}hrt$ Kant aus, so wie auch Leibniz, dass der intelligible Charakter des Menschen sich durch wiederholte freie Wahl formt, womit sich $best{\ddot{a}}tigt$, dass auch Kant die Freiheit der Wahl anerkannt hat. Kant leugnet die Wahlfreiheit, weil er der Ansicht ist, dass der Begriff der Freiheit als ein einheitlicher Begriff definiert werden muss. Doch Freiheit muss nicht zwingend einheitlich definiert werden. Da Freiheit von Zwang und Freiheit von Notwendigkeit nicht $widerspr{\ddot{u}}chliche$ Begriffe sind, $k{\ddot{o}}nnen$ sie dem selben Willen gleichzeitig zugeteilt werden. Auch wird erst hierdurch Autonomie $m{\ddot{o}}glich$ gemacht.

• Journal for History of Mathematics
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• v.19 no.1
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• pp.65-78
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• 2006

The law of refraction, which is called Snell's law in physics, has a significant meaning in mathematics history. After Snell empirically discovered the refraction law $\frac{v_1}{sin{\theta}_1}=\frac{v_2}{sin{\theta}_2$ through countless observations, many mathematicians endeavored to deduce it from the least time principle, and the need to surmount these difficulties was one of the driving forces behind the early development of calculus by Leibniz. Fermat solved it far advance of others by inventing a method that eventually led to the differential calculus. Historically, mathematics has developed in close connection with physics. Physics needs mathematics as an auxiliary discipline, but physics can also belong to the lived-through reality from which mathematics is provided with subject matters and suggestions. The refraction law is a suggestive example of interrelations between mathematical and physical theories. Freudenthal said that a purpose of mathematics education is to learn how to apply mathematics as well as to learn ready-made mathematics. I think that the refraction law could be a relevant content for this purpose. It is pedagogically sound to start in high school with a quasi-empirical approach to refraction. In college, mathematics and physics majors can study diverse mathematical proof including Fermat's original method in the context of discussing the phenomenon of refraction of light. This would be a ideal environment for such pursuit.

• Korean Journal of Logic
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• v.18 no.2
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• pp.217-241
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• 2015

Brandom upholds the anaphoric theory of reference. On this theory, reference is a relation of anaphoric dependence between linguistic items rather than a substantial relation between linguistic items and non-linguistic objects. In addition, 'refers' is a pronoun-forming operator, which is used to form anaphorically indirect descriptions such as 'the one referred to as "Leibniz"'. Recently, Arbid $B{\aa}ve$ raises three objections against this theory. First, the anaphoric theory distinguishes between ordinary descriptions and anaphorically indirect descriptions in terms of iterability. But this condition is not an adequate ground for asserting that anaphorically indirect descriptions form a distinctive semantic category. Second, sentences containing a pronoun such as 'he' and sentences containing an anaphorically indirect description such as 'the one referred to as "Leibniz"' have different modal statuses. Consequently, indirect descriptions are semantically different from paradigmatic anaphors. Third, on the anaphoric theory, expressions of the form 'a' and the corresponding indirect descriptions of the form 'the one referred to as "a"' are intersubstitutable. But we can make an equivalent claim by using the more general semantic concepts such as equivalence and intersubstitutability, instead of using notions such as 'anaphor' and 'antecedent'. So the anaphoric theory is explanatorily idle. In this paper I argue that these objections do not pose a serious problem for the anaphoric theory of reference. I argue thereby that the anaphoric theory of reference is a promising theory which provides us with the right understanding of the expression 'refers'.

• Journal of the Korean Society for Marine Environment & Energy
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• v.12 no.3
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• pp.165-172
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• 2009

A set of equations for description of transformation of harmonic waves is proposed here. Velocity potential function and separation of variables are introduced for the derivation. The continuity equation is in a vertical plane is integrated through the water so that a horizontal one-dimensional wave equation is produced. The new equation composed of the complex velocity potential function, further be modified into. A set up of equations composed of the wave amplitude and wave phase gradient. The horizontally one-dimensional equations on the wave amplitude and wave phase gradient are the first and second-order ordinary differential equations. They are solved in a one-way marching manner starting from a side where boundary values are supplied, i.e. the wave amplitude, the wave amplitude gradient, and the wave phase gradient. Simple spatially-centered finite difference schemes are adopted for the present set of equations. The equations set is applied to three test cases, Booij's inclined plane slope profile, Massel's smooth bed profile, and Bragg's wavy bed profile. The present equations set is satisfactorily verified against existing theories including Massel's modified mild-slope equation, Berkhoff's mild-slope equation, and the full linear equation.

• Journal of Korean Philosophical Society
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• v.123
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• pp.27-56
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• 2012

Das Ziel dieser Abhandlung ist die Unterscheidung zwischen der kognitiven und ontischen Ununterscheidbarkeit. Jene zeigt sich als die Ununterscheidbarkeit, die aus dem Fehler des Identifizierens erfolgt. Diese besteht in der $Selbstidentit{\ddot{a}}t$ jedes individuellen Seienden. Um der Untersuchung der zwei Arten der Ununterscheidbarkeit willen soll die $Identit{\ddot{a}}t$ als Begrifflichkeit von dem Identifizieren als der subjektiven $T{\ddot{a}}tigkeit$ unterschieden werden. $W{\ddot{a}}hrend$ das kognitiv Ununterscheidbare nicht immer das Identische sein kann, ist das ontisch Ununterscheidbare notwendig das Identische. Durch diese Unterscheidung zwischen den beiden Konzeptionen der Ununterscheidbarkeit kann der Sinn des Leibniz'schen Satzes der $Identit{\ddot{a}}t$ des Ununterscheidbaren (principium identitatisindiscernibilium) deutlicher erhellt werden, indem diese Unterscheidung die kritische $Verst{\ddot{a}}rkung$ seines Satzes impliziert. Die Denkbarkeit der Duplikate, die intrinsisch $v{\ddot{o}}llig$ identisch qualifiziert sind, gilt als der bedeutsamste Einwand gegen seinen Satz der $Identit{\ddot{a}}t$. Aber der $Identit{\ddot{a}}tssatz$ - principium identitatis indiscernibilium - ist noch $g{\ddot{u}}ltig$, weil diese Duplikate letztendlich mittels der raumzeitlichen Relationsbeschaffenheit unterscheidbar sind. Hierdurch wird die grundlegende bzw. unentbehrliche Funktion der $Subjektivit{\ddot{a}}t$, die die raumzeitliche Relationsbeschaffenheit $erm{\ddot{o}}glicht$, $erl{\ddot{a}}utert$. $Daf{\ddot{u}}r$ wird Hegels $Erkl{\ddot{a}}rung$ vom $Identit{\ddot{a}}tsbegriff$ und Leibniz bearbeitet.

• Biomolecules & Therapeutics
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• v.27 no.5
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• pp.492-501
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• 2019

Nitrogen-containing heterocycles such as quinoline, quinazolinones and indole are scaffolds of natural products and have broad biological effects. During the last years those structures have been intensively synthesized and modified to yield new synthetic molecules that can specifically inhibit the activity of dysregulated protein kinases in cancer cells. Herein, a series of newly synthesized isoquinolinamine (FX-1 to 8) and isoindoloquinazolinone (FX-9, FX-42, FX-43) compounds were evaluated in regards to their anti-leukemic potential on human B- and T- acute lymphoblastic leukemia (ALL) cells. Several biological effects were observed. B-ALL cells (SEM, RS4;11) were more sensitive against isoquinolinamine compounds than T-ALL cells (Jurkat, CEM). In SEM cells, metabolic activity decreased with $10{\mu}M$ up to 26.7% (FX-3), 25.2% (FX-7) and 14.5% (FX-8). The 3-(p-Tolyl) isoquinolin-1-amine FX-9 was the most effective agent against B- and T-ALL cells with IC50 values ranging from 0.54 to $1.94{\mu}M$. None of the tested compounds displayed hemolysis on erythrocytes or cytotoxicity against healthy leukocytes. Anti-proliferative effect of FX-9 was associated with changes in cell morphology and apoptosis induction. Further, influence of FX-9 on PI3K/AKT, MAPK and JAK/STAT signaling was detected but was heterogeneous. Functional inhibition testing of 58 kinases revealed no specific inhibitory activity among cancer-related kinases. In conclusion, FX-9 displays significant antileukemic activity in B- and T-ALL cells and should be further evaluated in regards to the mechanisms of action. Further compounds of the current series might serve as templates for the design of new compounds and as basic structures for modification approaches.