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Income taxes (Tables) | 6 Months Ended
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Jun. 30, 2024
Income taxes |
Component of Income Taxes Expenses | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Three months ended | ​ | Six months ended
​ | ​ | June 30, | ​ | June 30,
​ |  | 2023 |  | 2024 |  | 2023 |  | 2024
​ | ​ | (In millions)
Expected tax expense (benefit) at U.S. federal statutory income tax rate of 21% |  | $ | (1.4) | ​ | $ | 7.9 | ​ | $ | (3.5) | ​ | $ | 11.7
Non-U.S. tax rates | ​ |  | (2.4) | ​ |  | (.1) | ​ |  | (2.4) | ​ |  | (.1)
Incremental net tax benefit on earnings and losses of U.S. and non-U.S. tax group companies | ​ |  | (5.5) | ​ |  | (3.5) | ​ |  | (5.1) | ​ |  | (4.3)
Valuation allowance | ​ |  | — | ​ |  | 1.7 | ​ |  | — | ​ |  | 2.5
Global intangible low-tax income, net | ​ |  | 1.6 | ​ |  | 1.1 | ​ |  | .1 | ​ |  | 1.4
Adjustment to the reserve for uncertain tax positions, net | ​ |  | .7 | ​ |  | .1 | ​ |  | (.7) | ​ |  | .2
Adjustment of prior year taxes, net | ​ | ​ | — | ​ | ​ | — | ​ | ​ | (.4) | ​ | ​ | —
Nondeductible expenses | ​ | ​ | 1.0 | ​ | ​ | .4 | ​ | ​ | .5 | ​ | ​ | .6
U.S. state income taxes and other, net | ​ | ​ | (.8) | ​ | ​ | .3 | ​ | ​ | (.5) | ​ | ​ | .3
Income tax expense (benefit) | ​ | $ | (6.8) | ​ | $ | 7.9 | ​ | $ | (12.0) | ​ | $ | 12.3
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Comprehensive provision (benefit) for income taxes allocable to: | ​ |  |  | ​ |  |  | ​ |  |  | ​ |  |
Net income (loss) | ​ | $ | (6.8) | ​ | $ | 7.9 | ​ | $ | (12.0) | ​ | $ | 12.3
Other comprehensive income (loss): | ​ |  |  | ​ |  |  | ​ |  |  | ​ |  |
Currency translation | ​ |  | (.6) | ​ |  | .2 | ​ |  | (1.4) | ​ |  | (2.1)
Pension plans | ​ |  | .8 | ​ |  | .3 | ​ |  | 1.1 | ​ |  | .6
Other | ​ |  | (.1) | ​ |  | (.1) | ​ |  | (.3) | ​ |  | (.2)
Total | ​ | $ | (6.7) | ​ | $ | 8.3 | ​ | $ | (12.6) | ​ | $ | 10.6

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- Definition Tabular disclosure of the reconciliation using percentage or dollar amounts of the reported amount of income tax expense attributable to continuing operations for the year to the amount of income tax expense that would result from applying domestic federal statutory tax rates to pretax income from continuing operations. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Topic 740 -SubTopic 10 -Name Accounting Standards Codification -Paragraph 12 -Section 50 -Publisher FASB -URI https://asc.fasb.org//1943274/2147482685/740-10-50-12 + Details
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