Let
p
be a prime. We define
S
(
p
) the smallest number
k
such that every positive integer is a sum of at most
k
squares of integers that are not divisible by
p
. In this article, we prove that
S
(
2
...)
=
10
,
S
(
3
)
=
6
,
S
(
5
)
=
5
, and
S
(
p
)
=
4
for any prime
p
greater than 5. In particular, it is proved that every positive integer is a sum of at most four squares not divisible by 5, except the unique positive integer 79.
Frosting experiments were conducted on surface-treated (hydrophilic, hydrophobic, and dual) louvered-fin heat exchangers with varying fin pitches, and the frosting behavior of the rows was ...investigated in terms of the experimental conditions. In the early stage of experiments, three of these surface-treated heat exchangers exhibited the highest heat transfer rate at 16 FPI (fins per inch), in particular, the hydrophobic unit had the smallest reduction in the heat transfer rate during the latter stage due to the frost-retardation effect. Hence, the hydrophobic unit had the largest overall heat transfer rate. For the hydrophilic and dual-treated heat exchangers, the first row (front side) showed more active frost growth than the second row (rear side), and thus the leading-edge effect was demonstrated in these two heat exchangers. By contrast, with the hydrophobic heat exchanger, the leading-edge effect was not observed when the refrigerant temperature was higher than −10°C, or the airflow rate was higher. The ratio of remained water after defrosting was the highest for the hydrophobic unit, but this unit still showed the highest overall heat transfer rate during the repeated frosting and defrosting experiments cycle, due to frost retardation.
Studies on the age and generation characteristics of traffic accidents primarily focus on the tendency of deaths and severe injuries, whereas the faults or drivers who caused the accidents are not ...considered. Using license holders as a parameter for measuring accident risk when evaluating the number of primary-party accidents is challenging because it includes those who possess licenses but do not drive. In previous studies, the age characteristics in traffic accidents were evaluated based on different age groups and generational characteristics. Therefore, a Bayesian age–period–cohort analysis was performed in this study to isolate the effects of age, period, and generation on the number of traffic crashes. This approach can identify the gender/age of the driver, who may be the primary contributor to an accident, as well as the risk of traffic accidents in younger and older drivers. The results show that 1) age imposes a more significant effect than the duration and cohort. In the case of single-vehicle accidents, 2) the effect of age was significantly more prominent for males over 80 years old and females over 70 years old.
We aimed to assess cross-cultural differences in depressive symptoms and the validity of the Korean version of the Mood and Feelings Questionnaire (MFQ). Four hundred and sixty-four children and ...adolescents (aged 7–19, 278 girls) with any psychiatric diagnosis, 290 of whom had major depressive disorder, were included. The levels of depressive symptoms in children and adolescents were evaluated by children/adolescents and their parents. We conducted Pearson’s
r
and Cronbach’s α, confirmative factor analysis and item response theory tests. The Korean version of the MFQ demonstrated excellent criterion validity and discriminant validity. There were no cultural differences in the clinical manifestations of depression in youth from Western countries and Korea. Korean youths with depression were more likely to complain of cognitive and emotional symptoms than somatic symptoms. The Korean version of the MFQ demonstrated promising psychometric properties in a clinical sample of children and adolescents.
Polymer electrolytes are important materials in the manufacture of all-solid-state batteries due to their ionic conductivity, achieved by doping the polymer with salt, and mechanical strength, ...achieved by use of a block copolymer with a rigid block. High salt concentration is advantageous to achieve high ionic conductivity, but it makes estimation of battery performance difficult due to the breakdown of dilute-solution theory, which assumes complete ion dissociation. Therefore, practical battery design would benefit from an empirical understanding of the relationship between ion dissociation and salt concentration in block copolymer electrolyte. In this study, the dissociation of lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) in polystyrene (PS)—poly(ethylene oxide) (PEO) diblock copolymer electrolyte was investigated using Fourier transform infrared (FTIR) spectroscopy. Quantitative analysis was performed to reveal the appearance of ion pairs and interactions between the salt and the ethylene oxide moieties with increasing salt concentration. FTIR peaks associated with polymer functional groups were found to be more useful than those of the TFSI anion for understanding the chemical state of the block copolymer electrolyte. In particular, PS peaks were used to quantify polymer dilution upon salt addition and verify that the Beer–Lambert law was valid at all concentrations investigated. PEO peaks revealed conformational changes of the polymer upon coordination with lithium ions. A previously unidentified FTIR peak was discovered that relates to polymer–salt interaction. It was used to determine the extent of salt dissociation, which compares well with a Raman study of a homopolymer electrolyte. This work definitively shows that LiTFSI dissolves into the PEO phase of the block copolymer, essentially unaffected by PS presence. It also establishes FTIR as a useful technique for quantifying dissociation state of concentrated polymer and composite electrolytes for lithium batteries.
In this article, we prove that a space of cusp forms of weight 2 with level
N
and real character
χ
has dimension 1 if and only if
χ
is trivial and
N
is in
{
11
,
14
,
15
,
17
,
19
,
20
,
21
,
24
,
27
...,
32
,
36
,
49
}
,
and derive bases for spaces of cusp forms of weight 2 with trivial character and
N
∈
{
17
,
19
,
21
,
49
}
. As applications, we provide formulas for the number of representations of integers by 4-dimensional strongly
N
-modular lattices for
N
in
{
11
,
14
,
15
,
17
,
19
,
20
,
21
,
24
,
27
,
32
,
36
}
.
Let f be a positive definite integral quinary quadratic form. We say f is strongly s-regular if it satisfies a strong regularity property on the number of representations of squares of integers by f. ...In this article, we show that there exist exactly 19 strongly s-regular diagonal quinary quadratic forms representing 1 (see Table 1). In particular, we use eta-quotients of weight 52 to prove the strongly s-regularity of the quinary quadratic form x2+2y2+2z2+3w2+3t2, which is, in fact, of class number 4.
The utilization of multi-temporally integrated imageries, combined with advanced techniques such as convolutional neural networks (CNNs), has shown significant potential in enhancing the accuracy and ...efficiency of tree species classification models. In this study, we explore the application of CNNs for tree species classification using multi-temporally integrated imageries. By leveraging the temporal variations captured in the imageries, our goal is to improve the classification models’ discriminative power and overall performance. The results of our study reveal a notable improvement in classification accuracy compared to previous approaches. Specifically, when compared to the random forest model’s classification accuracy of 84.5% in the Gwangneung region, our CNN-based model achieved a higher accuracy of 90.5%, demonstrating a 6% improvement. Furthermore, by extending the same model to the Chuncheon region, we observed a further enhancement in accuracy, reaching 92.1%. While additional validation is necessary, these findings suggest that the proposed model can be applied beyond a single region, demonstrating its potential for a broader applicability. Our experimental results confirm the effectiveness of the deep learning approach in achieving a high accuracy in tree species classification. The integration of multi-temporally integrated imageries with a deep learning algorithm presents a promising avenue for advancing tree species classification, contributing to improved forest management, conservation, and monitoring in the context of a climate change.
It is essential in weapons systems to understand how much explosive power is applied according to various chemicals and methods of the explosion. In particular, to measure dynamic thermal phenomena ...and analyze thermal properties under high-temperature and high-pressure conditions. Although many researchers have used thermocouples to measure the temperature during an explosion, this method has an error in the temperature measurement as the radiant heat flux increases. Another measurement method is needed to solve this problem. During an explosion in a shock tube, the temperature change was measured with a thermocouple and a pressure sensor. To solve the limitations of the thermocouple’s measurement responsiveness in temperature measurement was compared with the TDLD (tunable diode laser detection) method. In the case of the TDLD method, the time to reach the peak was measured an average 0.0207 sec faster than the thermocouple. Moreover, the peak average temperature was 15.8 °C higher than that of the thermocouple.
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