• Journal of the Korean Magnetic Resonance Society
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• v.26 no.1
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• pp.10-16
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• 2022

The phase transition temperatures of CsCoCl₃·2H₂O crystals are investigated via differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA). Three endothermic peaks at temperatures of 370 K (=T_C1), 390 K (=T_C2), and 416 K (=T_C3) were observed for phase transitions from CsCoCl₃·2H₂O to CsCoCl₃·1.5H₂O, to CsCoCl₃·H₂O, and then to CsCoCl₃·0.5H₂O, respectively. In addition, the spin-lattice relaxation time T_1ρ in the rotating frame and T₁ in the laboratory frame as well as changes in chemical shifts for ¹H and ¹³³Cs near T_C1 were found to be temperature dependent. Our analyses results indicated that the changes of chemical shifts, T_1ρ, and T₁ are associated with structural phase transitions near temperature T_C1. The changes of chemical shifts, T_1ρ, and T₁ near T_C1 were associated with structural phase transitions, owing to the changes in the symmetry of the structure formed of H₂O and Cs⁺ ions. Consequently, the structural symmetry in CsCoCl₃·2H₂O crystals based on temperature is discussed by the environments of their H and Cs nuclei.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.30 no.5
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• pp.200-207
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• 2020

MoSi₂, (Mo_1/2W_1/2)Si₂, and WSi₂ powders were synthesized by self-propagating high-temperature synthesis (SHS) method. The synthesized powders were heat-treated at 500, 1,000, 1,200, 1,300, 1,400, 1,500 and 1,600℃ in ambient atmosphere. Oxidation of Mo-W silicide powder was found at low temperature of 500℃. XRD structure analysis and DTA/TG data showed that MoO₃ was formed with 500℃ heat treatment for 1 hour, and that it was α-cristobalite phase that was formed with 1200℃ heat treatment, not α-quartz phase which is commonly found and stable at room temperature. Existence of W accelerated decomposition at both low and high temperature. Fully sintered MoSi₂ and (Mo_1/2W_1/2)Si₂ specimen did not show decomposition or weight loss by oxidation, with 1 hour heat treatment at either low or high temperature. Notably, it was difficult to sinter WSi₂ because of oxidation reaction at low temperature.

• Korean Journal of Mineralogy and Petrology
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• v.35 no.2
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• pp.83-100
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• 2022

The Zhenzigou Pb-Zn deposit, which is one of the largest Pb-Zn deposit in the northeast of China, is located at the Qingchengzi mineral field in Jiao Liao Ji belt. The geology of this deposit consists of Archean granulite, Paleoproterozoinc migmatitic granite, Paleo-Mesoproterozoic sodic granite, Paleoproterozoic Liaohe group, Mesozoic diorite and Mesozoic monzoritic granite. The Zhenzigou deposit which is a strata bound SEDEX or SEDEX type deposit occurs as layer ore and vein ore in Langzishan formation and Dashiqiao formation of the Paleoproterozoic Liaohe group. White mica from this deposit are occured only in layer ore and are classified four type (Type I : weak alteration (clastic dolomitic marble), Type II : strong alteration (dolomitic clastic rock), Type III : layer ore (dolomitic clastic rock), Type IV : layer ore (clastic dolomitic marble)). Type I white mica in weak alteration zone is associated with dolomite that is formed by dolomitization of hydrothermal metasomatism. Type II white mica in strong alteration zone is associated with dolomite, ankerite, quartz and alteration of K-feldspar by hydrothermal metasomatism. Type III white mica in layer ore is associated with dolomite, ankerite, calcite, quartz and alteration of K-feldspar by hydrothermal metasomatism. And type IV white mica in layer ore is associated with dolomite, quartz and alteration of K-feldspar by hydrothermal metasomatism. The structural formulars of white micas are determined to be (K_0.92-0.80Na_0.01-0.00Ca_0.02-0.01Ba_0.00Sr_0.01-0.00)_0.95-0.83(Al_1.72-1.57Mg_0.33-0.20Fe_0.01-0.00Mn_0.00Ti_0.02-0.00Cr_0.01-0.00V_0.00Sb_0.02-0.00Ni_0.00Co_0.02-0.00)_1.99-1.90(Si_3.40-3.29Al_0.71-0.60)_4.00O₁₀(OH_2.00-1.83F_0.17-0.00)_2.00, (K_1.03-0.84Na_0.03-0.00Ca_0.08-0.00Ba_0.00Sr_0.01-0.00)_1.08-0.85(Al_1.85-1.65Mg_0.20-0.06Fe_0.10-0.03Mn_0.00Ti_0.05-0.00Cr_0.03-0.00V_0.01-0.00Sb_0.02-0.00Ni_0.00Co_0.03-0.00)_1.99-1.93(Si_3.28-2.99Al_1.01-0.72)_4.00O₁₀(OH_1.96-1.90F_0.10-0.04)_2.00, (K_1.06-0.90Na_0.01-0.00Ca_0.01-0.00Ba_0.00Sr_0.02-0.01)_1.10-0.93(Al_1.93-1.64Mg_0.19-0.00Fe_0.12-0.01Mn_0.00Ti_0.01-0.00Cr_0.01-0.00V_0.00Sb_0.00Ni_0.00Co_0.05-0.01)_2.01-1.94(Si_3.32-2.96Al_1.04-0.68)_4.00O₁₀(OH_2.00-1.91F_0.09-0.00)_2.00 and (K_0.91-0.83Na_0.02-0.01Ca_0.02-0.00Ba_0.01-0.00Sr_0.00)_0.93-0.83(Al_1.84-1.67Mg_0.15-0.08Fe_0.07-0.02Mn_0.00Ti_0.04-0.00Cr_0.06-0.00V_0.02-0.00Sb_0.02-0.01Ni_0.00Co_0.00)_2.00-1.92(Si_3.27-3.16Al_0.84-0.73)_4.00O₁₀(OH_1.97-1.88F_0.12-0.03)_2.00, respectively. It indicated that white mica of from the Zhenzigou deposit has less K, Na and Ca, and more Si than theoretical dioctahedral mica. Compositional variations in white mica from the Zhenzigou deposit are caused by phengitic or Tschermark substitution [(Al³⁺)^VI+(Al³⁺)^IV <-> (Fe²⁺ or Mg²⁺)^VI+(Si⁴⁺)^IV] substitution. It means that the Fe in white mica exists as Fe²⁺ and Fe³⁺, but mainly as Fe²⁺. Therefore, white mica from layer ore of the Zhenzigou deposit was formed in the process of remelting and re-precipitation of pre-existed minerals by hydrothermal metasomatism origined metamorphism (greenschist facies) associated with Paleoproterozoic intrusion. And compositional variations in white mica from the Zhenzigou deposit are caused by phengitic or Tschermark substitution [(Al³⁺)^VI+(Al³⁺)^IV <-> (Fe²⁺ or Mg²⁺)^VI+(Si⁴⁺)^IV] substitution during hydrothermal metasomatism depending on wallrock type, alteration degree and ore/gangue mineral occurrence frequency.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.1137-1150
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• 2022

Consider the quantum algebra U_q(sl₂) over field 𝓕 (char(𝓕) = 0) with equitable generators x^±1, y and z, where q is fixed nonzero, not root of unity scalar in 𝓕. Let V denote a finite dimensional irreducible module for this algebra. Let Λ ∈ End(V), and let {A₁, A₂, A₃} = {x, y, z}. First we show that if Λ, A₁ is a Leonard pair, then this Leonard pair have four types, and we show that for each type there exists a Leonard pair Λ, A₁ in which Λ is a linear combination of 1, A₂, A₃, A₂A₃. Moreover, we use Λ to construct 𝚼 ∈ U_q(sl₂) such that 𝚼, A^-1₁ is a Leonard pair, and show that 𝚼 = I + A₁Φ + A₁ΨA₁ where Φ and Ψ are linear combination of 1, A₂, A₃.

• Korean Journal of Mineralogy and Petrology
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• v.35 no.2
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• pp.125-140
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• 2022

The Xiquegou Pb-Zn deposit is located at the Qingchengzi orefield which is one of the largest Pb-Zn mineralized zone in the northeast of China. The geology of this deposit consists of Archean granulite, Paleoproterozoinc migmatitic granite, Paleo-Mesoproterozoic sodic granite, Paleoproterozoic Liaohe group, Mesozoic diorite and Mesozoic monzoritic granite. The Xiquegou deposit which is a Triassic magma-hydrothermal type deposit occurs as vein ore filled fractures along fault zone in unit 3 (dolomitic marble and schist) of Dashiqiao formation of the Paleoproterozoic Liaohe group. Xiquegou Pb-Zn deposit consists of quartz, apatite, calcite, pyrite, arsenopyrite, pyrrhotite, marcasite, sphalerite, chalcopyrite, stannite, galena, tetrahedrite, electrum, argentite, native silver and pyrargyrite. Wallrock alteration of this deposit contains silicification, pyritization, dolomitization, chloritization and sericitization. Based on mineral petrography and paragenesis, dolomites from this deposit are classified two type (1. dolomite (D₀) as wallrock, 2. dolomite (D₁) as wallrock alteration in Pb-Zn mineralization quartz vein ore). The structural formulars of dolomites are determined to be Ca_1.03-1.01Mg_0.95-0.83Fe_0.12-0.02Mn_0.02-0.00(CO₃)₂(D₀) and Ca_1.16-1.00Mg_0.79-0.44Fe_0.53-0.13Mn_0.03-0.00As_0.01-0.00(CO₃)₂(D₁), respectively. It means that dolomites from the Xiquegou deposit have higher content of trace elements compared to the theoretical composition of dolomite. The dolomite (D₁) from quartz vein ore has higher content of these trace elements (FeO, PbO, Sb₂O₅ and As₂O₅) than dolomite (D₀) from wallrock. Dolomites correspond to Ferroan dolomite (D₀), and ankerite and Ferroan dolomite (D₁), respectively. The structural formular of chlorite from quartz vein ore is (Mg_1.65-1.08Fe_2.94-2.50Mn_0.01-0.00Zn_0.01-0.00Ni_0.01-0.00Cr_0.02-0.00V_0.01-0.00Hf_0.01-0.00Pb_0.01-0.00Cu_0.01-0.00As_0.03-0.00Ca_0.02-0.01Al_1.68-1.61)_5.77-5.73(Si_2.84-2.76Al_1.24-1.16)_4.00O₁₀(OH)₈. It indicated that chlorite of quartz vein ore is similar with theoretical chlorite and corresponds to Fe-rich chlorite. Compositional variations in chlorite from quartz vein ore are caused by mainly octahedral Fe²⁺ <-> Mg²⁺ (Mn²⁺) substitution and partly phengitic or Tschermark substitution (Al^3+,VI+Al^3+,IV <-> (Fe²⁺ 또는 Mg²⁺)^VI+(Si⁴⁺)^IV).

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.915-937
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• 2021

In this paper we deal with the open problem posed by Lü, Li and Yang [10]. In fact, we prove the following result: Let f(z) be a transcendental meromorphic function of finite order having finitely many poles, c₁, c₂, …, c_n ∈ ℂ\{0} and k, n ∈ ℕ. Suppose fⁿ(z), f(z+c₁)f(z+c₂) ⋯ f(z+c_n) share 0 CM and fⁿ(z)-Q₁(z), (f(z+c₁)f(z+c₂) ⋯ f(z+c_n))^(k) - Q₂(z) share (0, 1), where Q₁(z) and Q₂(z) are non-zero polynomials. If n ≥ k+1, then $(f(z+c_1)f(z+c_2)\;{\cdots}\;f(z+c_n))^{(k)}\;{\equiv}\;{\frac{Q_2(z)}{Q_1(z)}}f^n(z)$. Furthermore, if Q₁(z) ≡ Q₂(z), then $f(z)=c\;e^{\frac{\lambda}{n}z}$, where c, λ ∈ ℂ \ {0} such that e^{λ(c₁+c₂+⋯+c_n)} = 1 and λ^k = 1. Also we exhibit some examples to show that the conditions of our result are the best possible.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.711-720
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• 2021

Let R denote a commutative noetherian ring, and let 𝐱 := x1, …, xd be an R-regular sequence. Suppose that 𝖆 denotes a monomial ideal with respect to 𝐱. The first purpose of this article is to show that 𝖆 is irreducible if and only if 𝖆 is a generalized-parametric ideal. Next, it is shown that, for any integer n ≥ 1, (x1, …, xd)n = ⋂P(f), where the intersection (irredundant) is taken over all monomials f = xe11 ⋯ xedd such that deg(f) = n - 1 and P(f) := (xe1+11, ⋯, xed+1d). The second main result of this paper shows that if 𝖖 := (𝐱) is a prime ideal of R which is contained in the Jacobson radical of R and R is 𝖖-adically complete, then 𝖆 is a parameter ideal if and only if 𝖆 is a monomial irreducible ideal and Rad(𝖆) = 𝖖. In addition, if a is generated by monomials m1, …, mr, then Rad(𝖆), the radical of a, is also monomial and Rad(𝖆) = (ω1, …, ωr), where ωi = rad(mi) for all i = 1, …, r.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.257-267
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• 2016

We find examples of Ideals in a tridiagonal algebra ALGL_∞ and study some properties of Ideals in ALGL_∞. We prove the following theorems: Let k and j be fixed natural numbers. Let A be a subalgebra of ALGL_∞ and let A_2,{k} ⊂ A ⊂ {T ∈ ALGL_∞ | T_(2k-1,2k) = 0}. Then A is an ideal of ALGL_∞ if and only if A = A_2,{k} where A_2,{k} = {T ∈ ALGL_∞ | T_(2k-1,2k) = 0, T_(2k-1,2k-1) = T_(2k,2k) = 0}. Let B be a subalgebra of ALGL_∞ such that B_2,{j} ⊂ B ⊂ {T ∈ ALGL_∞ | T_(2j+1,2j) = 0}. Then B is an ideal of ALGL_∞ if and only if B = B_2,{j}, where B_2,{j} = {T ∈ ALGL_∞ | T_(2j+1,2j) = 0, T_(2j,2j) = T_(2j+1,2j+1) = 0}.

• Korean Journal of Mineralogy and Petrology
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• v.34 no.3
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• pp.177-191
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• 2021

The Zhenzigou Pb-Zn deposit, one of the largest Pb-Zn deposit in the northeast of China, is located at the Qingchengzi mineral field in Jiao Liao Ji belt. The geology of this deposit consists of Archean granulite, Paleoproterozoinc migmatitic granite, Paleo-Mesoproterozoic sodic granite, Paleoproterozoic Liaohe group, Mesozoic diorite and monzoritic granite. The Zhenzigou deposit which is a strata bound SEDEX or SEDEX type deposit occurs as layer ore and vein ore in Langzishan formation and Dashiqiao formation of the Paleoproterozoic Liaohe group. Based on mineral petrography and paragenesis, dolomites from this deposit are classified three type (1. dolomite (D₀) as hostrock, 2. dolomite (D₁) in layer ore associated with white mica, quartz, K-feldspar, sphalerite, galena, pyrite, arsenopyrite from greenschist facies, 3. dolomite (D₂) in vein ore associated with quartz, apatite and pyrite from quartz vein). The structural formulars of dolomites are determined to be Ca_1.00-1.03Mg_0.94-0.98Fe_0.00-0.06As_0.00-0.01(CO₃)₂(D₀), Ca_0.97-1.16Mg_0.32-0.83Fe_0.10-0.50Mn_0.01-0.12Zn_0.00-0.01Pb_0.00-0.03As_0.00-0.01(CO₃)₂(D₁), Ca_1.00-1.01Mg_0.85-0.92Fe_0.06-0.11 Mn_0.01-0.03As_0.01(CO₃)₂(D₂), respectively. It means that dolomites from the Zhenzigou deposit have higher content of trace elements compared to the theoretical composition of dolomite. Feo and MnO contents of these dolomites (D₀, D₁ and D₂) contain 0.05-2.06 wt.%, 0.00-0.08 wt.% (D₀), 3.53-17.22 wt.%, 0.49-3.71 wt.% (D₁) and 2.32-3.91 wt.%, 0.43-0.95 wt.% (D₂), respectively. The dolomite (D₁) from layer ore has higher content of these trace elements (FeO, MnO, ZnO and PbO) than dolomite (D₀) from hostrock and dolomite (D₂) from quartz vein. Dolomites correspond to Ferroan dolomite (D₀ and D₂), and ankerite and Ferroan dolomite (D₁), respectively. Therefore, 1) dolomite (D₀) from hostrock is a Ferroan dolomite formed by marine evaporative lagoon environment in Paleoproterozoic Jiao Liao Ji basin. 2) Dolomite (D₁) from layer ore is a ankerite and Ferroan dolomite formed by hydrothermal metasomatism origined metamorphism (greenschist facies) associated with Paleoproterozoic intrusion. 3) Dolomte (D₂) from quartz vein is a Ferroan dolomite formed by hydrothermal fluid origined Mesozoic intrusion.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1221-1244
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• 2020

In this paper we consider L_K-conjecture introduced in [5, 6] for hypersurface Mⁿ in space form Rⁿ⁺¹(c) with three principal curvatures. When c = 0, -1, we show that every L₁-biharmonic hypersurface with three principal curvatures and H₁ is constant, has H₂ = 0 and at least one of the multiplicities of principal curvatures is one, where H₁ and H₂ are first and second mean curvature of M and we show that there is not L₂-biharmonic hypersurface with three disjoint principal curvatures and, H₁ and H₂ is constant. For c = 1, by considering having three principal curvatures, we classify L₁-biharmonic hypersurfaces with multiplicities greater than one, H₁ is constant and H₂ = 0, proper L₁-biharmonic hypersurfaces which H₁ is constant, and L₂-biharmonic hypersurfaces which H₁ and H₂ is constant.